An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
Алгоритмическое введение в численное моделирование стохастических дифференциальных уравнений
2001-01-01
SCID: 54.1/shu9zbsg
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Euler–Maruyama methodMilstein’s methodstochastic differential equationsstochastic integrationstrong and weak convergence
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Abstract (AI)
Abstract. A practical and accessible introduction to numerical methods for stochastic differential equations is given. The reader is assumed to be familiar with Euler’s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable; however, no knowledge of advanced probability theory or stochastic processes is assumed. The article is built around 10 MATLAB programs, and the topics covered include stochastic integration, the Euler–Maruyama method, Milstein’s method, strong and weak convergence, linear stability, and the stochastic chain rule.
Key Findings
1
It develops the presentation around 10 MATLAB programs to support algorithmic understanding and implementation.
2
The article provides a practical, accessible introduction to numerical simulation methods for stochastic differential equations.
3
The covered methods include stochastic integration, Euler–Maruyama, Milstein’s method, strong and weak convergence, linear stability, and the stochastic chain rule.
4
The exposition assumes familiarity with deterministic Euler’s method and intuitive random-variable concepts, without requiring advanced probability or stochastic-process theory.
Research Object
Numerical simulation methods for stochastic differential equations (SDEs)
Research Subject
stochastic integration, numerical approximation methods, convergence, stability, and the stochastic chain rule
Publication Details
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2001-01-01
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