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This chapter presents an introduction to stochastic calculus for processes in continuous time and continuous event spaces. Starting from the Wiener process, it introduces the basic definitions and formulas of the Itô calculus and processes, and the distributional dynamics tools for their characterization, in particular the Fokker-Planck-Kolmogorov and the backward Kolmogorov equations.

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Introduction to Stochastic Calculus and Stochastic Differential Equations

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  • 发表日期：

    2026年

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  • Paulo B. Brito

摘要

This chapter presents an introduction to stochastic calculus for processes in continuous time and continuous event spaces. Starting from the Wiener process, it introduces the basic definitions and formulas of the Itô calculus and processes, and the distributional dynamics tools for their characterization, in particular the Fokker-Planck-Kolmogorov and the backward Kolmogorov equations.