# Continuous Time Stochastic Processes ⎊ Area ⎊ Greeks.live --- ## What is the Process of Continuous Time Stochastic Processes? Continuous Time Stochastic Processes, within the context of cryptocurrency, options trading, and financial derivatives, represent a mathematical framework for modeling phenomena evolving continuously over time, where future states are inherently uncertain. These processes are fundamental to pricing exotic options, managing risk in volatile crypto markets, and developing sophisticated trading strategies. Unlike discrete-time models, they capture the dynamic nature of asset prices and market conditions with greater fidelity, allowing for a more nuanced understanding of derivative valuation and hedging. The framework is particularly relevant given the high-frequency trading and rapid price fluctuations characteristic of digital assets. ## What is the Application of Continuous Time Stochastic Processes? The application of Continuous Time Stochastic Processes extends across various areas, including the Black-Scholes model for option pricing, which relies on the assumption of geometric Brownian motion for asset prices. In cryptocurrency, these models are adapted to account for factors like volatility skew, liquidity constraints, and the potential for sudden regulatory changes. Furthermore, they underpin the development of more complex derivative products, such as variance swaps and Asian options, frequently traded on crypto exchanges. Sophisticated risk management techniques, including Value at Risk (VaR) and Expected Shortfall (ES), also leverage these processes for accurate assessment. ## What is the Analysis of Continuous Time Stochastic Processes? Analysis using Continuous Time Stochastic Processes often involves techniques from stochastic calculus, such as Ito's Lemma, to derive pricing equations and hedging strategies. The efficiency of these models hinges on the accuracy of the underlying assumptions, particularly regarding the distributional properties of asset returns. Model risk, arising from deviations between the theoretical model and real-world market behavior, is a critical consideration, especially in the nascent and rapidly evolving cryptocurrency space. Robust backtesting and sensitivity analysis are essential for validating model performance and identifying potential vulnerabilities. --- ## [Brownian Motion Modeling](https://term.greeks.live/term/brownian-motion-modeling/) Meaning ⎊ Brownian motion modeling provides the quantitative foundation for valuing risk and uncertainty within decentralized derivative market structures. ⎊ Term ## [Continuous Trading Systems](https://term.greeks.live/term/continuous-trading-systems/) Meaning ⎊ Continuous Trading Systems provide the essential infrastructure for real-time price discovery and risk management in decentralized derivative markets. ⎊ Term ## [Continuous Trading Alternatives](https://term.greeks.live/definition/continuous-trading-alternatives/) Market models like batch auctions that replace instant matching with grouped execution to improve stability and fairness. ⎊ Term ## [Continuous Delivery Security](https://term.greeks.live/term/continuous-delivery-security/) Meaning ⎊ Continuous Delivery Security provides the automated cryptographic framework necessary to maintain protocol integrity during rapid financial iteration. ⎊ Term ## [Discrete Time Stochastic Processes](https://term.greeks.live/definition/discrete-time-stochastic-processes/) Mathematical frameworks modeling random price changes occurring at fixed time intervals to simplify complex system analysis. ⎊ Term ## [Continuous Risk Calculation](https://term.greeks.live/term/continuous-risk-calculation/) Meaning ⎊ Continuous Risk Calculation enables real-time solvency enforcement by dynamically adjusting margin requirements to match market volatility and risk. ⎊ Term ## [Continuous Integration Security Pipelines](https://term.greeks.live/definition/continuous-integration-security-pipelines/) Automated workflows that integrate security checks into every stage of the software development lifecycle. ⎊ Term ## [Continuous-Time Financial Models](https://term.greeks.live/term/continuous-time-financial-models/) Meaning ⎊ Continuous-Time Financial Models provide the mathematical framework for valuing derivatives and managing risk within fluid, decentralized markets. ⎊ Term ## [Continuous Integration Security](https://term.greeks.live/term/continuous-integration-security/) Meaning ⎊ Continuous Integration Security automates the cryptographic verification of financial protocols to ensure systemic stability in decentralized markets. ⎊ Term ## [On Chain Governance Processes](https://term.greeks.live/term/on-chain-governance-processes/) Meaning ⎊ On Chain Governance Processes automate protocol decision-making to ensure secure, transparent, and resilient decentralized financial operations. ⎊ Term ## [Securitization Processes](https://term.greeks.live/term/securitization-processes/) Meaning ⎊ Securitization processes convert heterogeneous crypto assets into structured, risk-defined instruments to optimize capital allocation and liquidity. ⎊ Term ## [Trade Confirmation Processes](https://term.greeks.live/term/trade-confirmation-processes/) Meaning ⎊ Trade Confirmation Processes establish the cryptographic finality and binding verification required for secure, decentralized derivative settlement. ⎊ Term ## [Network Upgrade Processes](https://term.greeks.live/term/network-upgrade-processes/) Meaning ⎊ Network Upgrade Processes serve as systemic calibration events that redefine protocol parameters and dictate risk profiles for derivative instruments. ⎊ Term ## [Settlement Processes](https://term.greeks.live/term/settlement-processes/) Meaning ⎊ Settlement processes provide the essential cryptographic and mechanical finality required to transform speculative derivative contracts into realized value. ⎊ Term ## [On-Chain Verification Processes](https://term.greeks.live/term/on-chain-verification-processes/) Meaning ⎊ On-chain verification processes provide the cryptographic foundation for secure, autonomous, and trustless settlement of decentralized derivatives. ⎊ Term ## [Block Validation Processes](https://term.greeks.live/term/block-validation-processes/) Meaning ⎊ Block validation processes provide the deterministic settlement layer necessary for the integrity and pricing of decentralized derivative instruments. ⎊ Term ## [Validator Selection Processes](https://term.greeks.live/term/validator-selection-processes/) Meaning ⎊ Validator selection processes provide the economic and algorithmic framework that determines participant authority in decentralized consensus. ⎊ Term ## [Data Reconciliation Processes](https://term.greeks.live/term/data-reconciliation-processes/) Meaning ⎊ Data reconciliation processes provide the essential verification layer ensuring accurate state alignment for robust decentralized derivative markets. ⎊ Term ## [Protocol Amendment Processes](https://term.greeks.live/term/protocol-amendment-processes/) Meaning ⎊ Protocol Amendment Processes provide the essential, transparent mechanisms for decentralized systems to evolve their logic and parameters securely. ⎊ Term ## [Asset Tokenization Processes](https://term.greeks.live/term/asset-tokenization-processes/) Meaning ⎊ Asset tokenization converts rights to tangible assets into programmable digital tokens, enabling automated settlement and enhanced capital efficiency. ⎊ Term ## [On-Chain Liquidation Processes](https://term.greeks.live/term/on-chain-liquidation-processes/) Meaning ⎊ On-Chain Liquidation Processes provide the essential automated enforcement required to maintain protocol solvency in decentralized credit markets. ⎊ Term ## [Proposal Submission Processes](https://term.greeks.live/term/proposal-submission-processes/) Meaning ⎊ Proposal submission processes provide the necessary structural framework to govern and secure the evolution of decentralized financial protocols. ⎊ Term ## [Continuous Limit Order Book Alternative](https://term.greeks.live/term/continuous-limit-order-book-alternative/) Meaning ⎊ These protocols redefine market liquidity by replacing manual order matching with algorithmic pools that ensure continuous, deterministic execution. ⎊ Term ## [Continuous Time Pricing Simulation](https://term.greeks.live/term/continuous-time-pricing-simulation/) Meaning ⎊ Continuous Time Pricing Simulation provides the mathematical rigor to value complex crypto derivatives by modeling price paths as stochastic processes. ⎊ Term ## [Automated Financial Processes](https://term.greeks.live/term/automated-financial-processes/) Meaning ⎊ Automated financial processes replace manual oversight with deterministic code to ensure stable, efficient, and transparent crypto derivative settlement. ⎊ Term ## [Continuous Time Models](https://term.greeks.live/term/continuous-time-models/) Meaning ⎊ Continuous Time Models provide the mathematical foundation for pricing and managing risk in seamless, high-performance decentralized markets. ⎊ Term ## [Automated Governance Processes](https://term.greeks.live/term/automated-governance-processes/) Meaning ⎊ Automated Governance Processes programmatically manage derivative protocol risk, ensuring solvency through algorithmic, real-time parameter adjustment. ⎊ Term ## [Secure Boot Processes](https://term.greeks.live/term/secure-boot-processes/) Meaning ⎊ Secure Boot Processes provide the cryptographic foundation ensuring node integrity, preventing unauthorized code execution in decentralized networks. ⎊ Term ## [Identity Verification Processes](https://term.greeks.live/term/identity-verification-processes/) Meaning ⎊ Identity verification processes bridge decentralized trading with global regulatory frameworks to ensure counterparty legitimacy and systemic safety. ⎊ Term ## [Continuous Vesting](https://term.greeks.live/definition/continuous-vesting/) A model releasing tokens in real-time, block-by-block, ensuring maximum liquidity and minimal market disruption. ⎊ Term --- ## Raw Schema Data ```json { "@context": "https://schema.org", "@type": "BreadcrumbList", "itemListElement": [ { "@type": "ListItem", "position": 1, "name": "Home", "item": "https://term.greeks.live/" }, { "@type": "ListItem", "position": 2, "name": "Area", "item": "https://term.greeks.live/area/" }, { "@type": "ListItem", "position": 3, "name": "Continuous Time Stochastic Processes", "item": "https://term.greeks.live/area/continuous-time-stochastic-processes/" } ] } ``` ```json { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [ { "@type": "Question", "name": "What is the Process of Continuous Time Stochastic Processes?", "acceptedAnswer": { "@type": "Answer", "text": "Continuous Time Stochastic Processes, within the context of cryptocurrency, options trading, and financial derivatives, represent a mathematical framework for modeling phenomena evolving continuously over time, where future states are inherently uncertain. 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The plate's center features inner green and outer dark blue rings." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/validator-selection-processes/", "url": "https://term.greeks.live/term/validator-selection-processes/", "headline": "Validator Selection Processes", "description": "Meaning ⎊ Validator selection processes provide the economic and algorithmic framework that determines participant authority in decentralized consensus. ⎊ Term", "datePublished": "2026-03-23T07:35:46+00:00", "dateModified": "2026-03-23T07:37:07+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/tokenomics-and-exotic-derivatives-portfolio-structuring-visualizing-asset-interoperability-and-hedging-strategies.jpg", "width": 3850, "height": 2166, "caption": "A row of sleek, rounded objects in dark blue, light cream, and green are arranged in a diagonal pattern, creating a sense of sequence and depth. The different colored components feature subtle blue accents on the dark blue items, highlighting distinct elements in the array." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/data-reconciliation-processes/", "url": "https://term.greeks.live/term/data-reconciliation-processes/", "headline": "Data Reconciliation Processes", "description": "Meaning ⎊ Data reconciliation processes provide the essential verification layer ensuring accurate state alignment for robust decentralized derivative markets. ⎊ Term", "datePublished": "2026-03-23T06:03:22+00:00", "dateModified": "2026-03-23T06:04:16+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-smart-contract-execution-simulating-decentralized-exchange-liquidity-protocol-interoperability-and-dynamic-risk-management.jpg", "width": 3850, "height": 2166, "caption": "A macro abstract digital rendering features dark blue flowing surfaces meeting at a central glowing green mechanism. The structure suggests a dynamic, multi-part connection, highlighting a specific operational point." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/protocol-amendment-processes/", "url": "https://term.greeks.live/term/protocol-amendment-processes/", "headline": "Protocol Amendment Processes", "description": "Meaning ⎊ Protocol Amendment Processes provide the essential, transparent mechanisms for decentralized systems to evolve their logic and parameters securely. ⎊ Term", "datePublished": "2026-03-22T19:31:34+00:00", "dateModified": "2026-03-22T19:32:00+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-execution-and-multi-asset-hedging-strategies-in-decentralized-finance-protocol-layers.jpg", "width": 3850, "height": 2166, "caption": "A close-up view reveals a stylized, layered inlet or vent on a dark blue, smooth surface. The structure consists of several rounded elements, transitioning in color from a beige outer layer to dark blue, white, and culminating in a vibrant green inner component." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/asset-tokenization-processes/", "url": "https://term.greeks.live/term/asset-tokenization-processes/", "headline": "Asset Tokenization Processes", "description": "Meaning ⎊ Asset tokenization converts rights to tangible assets into programmable digital tokens, enabling automated settlement and enhanced capital efficiency. ⎊ Term", "datePublished": "2026-03-21T18:54:17+00:00", "dateModified": "2026-03-21T18:54:59+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/advanced-collateralization-and-cryptographic-security-protocols-in-smart-contract-options-derivatives-trading.jpg", "width": 3850, "height": 2166, "caption": "A high-tech stylized padlock, featuring a deep blue body and metallic shackle, symbolizes digital asset security and collateralization processes. A glowing green ring around the primary keyhole indicates an active state, representing a verified and secure protocol for asset access." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/on-chain-liquidation-processes/", "url": "https://term.greeks.live/term/on-chain-liquidation-processes/", "headline": "On-Chain Liquidation Processes", "description": "Meaning ⎊ On-Chain Liquidation Processes provide the essential automated enforcement required to maintain protocol solvency in decentralized credit markets. ⎊ Term", "datePublished": "2026-03-21T13:25:22+00:00", "dateModified": "2026-03-21T13:25:50+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/advanced-smart-contract-architecture-visualizing-collateralized-debt-position-dynamics-and-liquidation-risk-parameters.jpg", "width": 3850, "height": 2166, "caption": "A digitally rendered mechanical object features a green U-shaped component at its core, encased within multiple layers of white and blue elements. The entire structure is housed in a streamlined dark blue casing." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/proposal-submission-processes/", "url": "https://term.greeks.live/term/proposal-submission-processes/", "headline": "Proposal Submission Processes", "description": "Meaning ⎊ Proposal submission processes provide the necessary structural framework to govern and secure the evolution of decentralized financial protocols. ⎊ Term", "datePublished": "2026-03-21T07:27:13+00:00", "dateModified": "2026-03-21T07:41:11+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-finance-options-structuring-complex-collateral-layers-and-senior-tranches-risk-mitigation-protocol.jpg", "width": 3850, "height": 2166, "caption": "A macro view displays two nested cylindrical structures composed of multiple rings and central hubs in shades of dark blue, light blue, deep green, light green, and cream. The components are arranged concentrically, highlighting the intricate layering of the mechanical-like parts." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/continuous-limit-order-book-alternative/", "url": "https://term.greeks.live/term/continuous-limit-order-book-alternative/", "headline": "Continuous Limit Order Book Alternative", "description": "Meaning ⎊ These protocols redefine market liquidity by replacing manual order matching with algorithmic pools that ensure continuous, deterministic execution. ⎊ Term", "datePublished": "2026-03-21T02:29:35+00:00", "dateModified": "2026-03-21T02:30:30+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-perpetual-swaps-liquidity-provision-and-hedging-strategy-evolution-in-decentralized-finance.jpg", "width": 3850, "height": 2166, "caption": "A macro-photographic perspective shows a continuous abstract form composed of distinct colored sections, including vibrant neon green and dark blue, emerging into sharp focus from a blurred background. The helical shape suggests continuous motion and a progression through various stages or layers." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/continuous-time-pricing-simulation/", "url": "https://term.greeks.live/term/continuous-time-pricing-simulation/", "headline": "Continuous Time Pricing Simulation", "description": "Meaning ⎊ Continuous Time Pricing Simulation provides the mathematical rigor to value complex crypto derivatives by modeling price paths as stochastic processes. ⎊ Term", "datePublished": "2026-03-20T22:46:22+00:00", "dateModified": "2026-03-20T22:47:15+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/interlocking-derivative-market-dynamics-analyzing-options-pricing-and-implied-volatility-via-smart-contracts.jpg", "width": 3850, "height": 2166, "caption": "A close-up view presents two interlocking rings with sleek, glowing inner bands of blue and green, set against a dark, fluid background. The rings appear to be in continuous motion, creating a visual metaphor for complex systems." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/automated-financial-processes/", "url": "https://term.greeks.live/term/automated-financial-processes/", "headline": "Automated Financial Processes", "description": "Meaning ⎊ Automated financial processes replace manual oversight with deterministic code to ensure stable, efficient, and transparent crypto derivative settlement. ⎊ Term", "datePublished": "2026-03-20T21:44:33+00:00", "dateModified": "2026-03-20T21:45:48+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/algorithmic-high-frequency-trading-protocol-layers-demonstrating-decentralized-options-collateralization-and-data-flow.jpg", "width": 3850, "height": 2166, "caption": "A 3D render displays a futuristic mechanical structure with layered components. The design features smooth, dark blue surfaces, internal bright green elements, and beige outer shells, suggesting a complex internal mechanism or data flow." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/continuous-time-models/", "url": "https://term.greeks.live/term/continuous-time-models/", "headline": "Continuous Time Models", "description": "Meaning ⎊ Continuous Time Models provide the mathematical foundation for pricing and managing risk in seamless, high-performance decentralized markets. ⎊ Term", "datePublished": "2026-03-20T13:58:44+00:00", "dateModified": "2026-03-20T14:00:09+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/abstract-visual-representation-of-layered-financial-derivatives-risk-stratification-and-cross-chain-liquidity-flow-dynamics.jpg", "width": 3850, "height": 2166, "caption": "A close-up view shows overlapping, flowing bands of color, including shades of dark blue, cream, green, and bright blue. The smooth curves and distinct layers create a sense of movement and depth, representing a complex financial system." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/automated-governance-processes/", "url": "https://term.greeks.live/term/automated-governance-processes/", "headline": "Automated Governance Processes", "description": "Meaning ⎊ Automated Governance Processes programmatically manage derivative protocol risk, ensuring solvency through algorithmic, real-time parameter adjustment. ⎊ Term", "datePublished": "2026-03-20T12:23:39+00:00", "dateModified": "2026-03-20T12:24:08+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-finance-layered-architecture-visualization-complex-smart-contract-execution-flow-nested-derivatives-mechanism.jpg", "width": 3850, "height": 2166, "caption": "A detailed view of a complex, layered mechanical object featuring concentric rings in shades of blue, green, and white, with a central tapered component. The structure suggests precision engineering and interlocking parts." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/secure-boot-processes/", "url": "https://term.greeks.live/term/secure-boot-processes/", "headline": "Secure Boot Processes", "description": "Meaning ⎊ Secure Boot Processes provide the cryptographic foundation ensuring node integrity, preventing unauthorized code execution in decentralized networks. ⎊ Term", "datePublished": "2026-03-20T11:03:15+00:00", "dateModified": "2026-03-20T11:04:17+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/layered-financial-engineering-depicting-digital-asset-collateralization-in-a-sophisticated-derivatives-framework.jpg", "width": 3850, "height": 2166, "caption": "A detailed close-up shot of a sophisticated cylindrical component featuring multiple interlocking sections. The component displays dark blue, beige, and vibrant green elements, with the green sections appearing to glow or indicate active status." } }, { "@type": "Article", "@id": "https://term.greeks.live/term/identity-verification-processes/", "url": "https://term.greeks.live/term/identity-verification-processes/", "headline": "Identity Verification Processes", "description": "Meaning ⎊ Identity verification processes bridge decentralized trading with global regulatory frameworks to ensure counterparty legitimacy and systemic safety. ⎊ Term", "datePublished": "2026-03-19T19:15:20+00:00", "dateModified": "2026-03-19T19:15:41+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/decentralized-finance-layered-architecture-visualization-complex-smart-contract-execution-flow-nested-derivatives-mechanism.jpg", "width": 3850, "height": 2166, "caption": "A detailed view of a complex, layered mechanical object featuring concentric rings in shades of blue, green, and white, with a central tapered component. The structure suggests precision engineering and interlocking parts." } }, { "@type": "Article", "@id": "https://term.greeks.live/definition/continuous-vesting/", "url": "https://term.greeks.live/definition/continuous-vesting/", "headline": "Continuous Vesting", "description": "A model releasing tokens in real-time, block-by-block, ensuring maximum liquidity and minimal market disruption. ⎊ Term", "datePublished": "2026-03-19T12:25:01+00:00", "dateModified": "2026-03-19T12:26:07+00:00", "author": { "@type": "Person", "name": "Greeks.live", "url": "https://term.greeks.live/author/greeks-live/" }, "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/automated-yield-generation-protocol-mechanism-illustrating-perpetual-futures-rollover-and-liquidity-pool-dynamics.jpg", "width": 3850, "height": 2166, "caption": "The image portrays a sleek, automated mechanism with a light-colored band interacting with a bright green functional component set within a dark framework. This abstraction represents the continuous flow inherent in decentralized finance protocols and algorithmic trading systems." } } ], "image": { "@type": "ImageObject", "url": "https://term.greeks.live/wp-content/uploads/2025/12/complex-decentralized-finance-structured-products-intertwined-asset-bundling-risk-exposure-visualization.jpg" } } ``` --- **Original URL:** https://term.greeks.live/area/continuous-time-stochastic-processes/