An algorithmic introduction to numerical simulation of stochastic differential equations. (English) Zbl 0979.65007

Higham, Desmond J.

SIAM Rev. 43, No. 3, 525-546 (2001).

Summary: 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.

MSC:

65C30	Numerical solutions to stochastic differential and integral equations
60-04	Software, source code, etc. for problems pertaining to probability theory
65L06	Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H35	Computational methods for stochastic equations (aspects of stochastic analysis)
34F05	Ordinary differential equations and systems with randomness

Keywords:

Euler-Maruyama method; MATLAB; Milstein method; Monte Carlo method; stochastic simulation; strong and weak convergence; stochastic differential equations; linear stability

Software:

Matlab