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Stability analysis of numerical schemes for stochastic differential equations. (English) Zbl 0869.60052
A linear stability analysis is discussed for numerical discrete time solution methods of ItĂ´ differential equations. The function which defines a recursion between the second moments of the approximations in the steps \(n\) and \(n+1\) is called the stability function of the numerical scheme. A scheme is called mean square stable if the absolute value of the stability function is less than 1. Stability functions and regions are determined for schemes of Euler and Heun type. The paper contains also results of numerical experiments.
Reviewer: W.Grecksch (Halle)

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C99 Probabilistic methods, stochastic differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
65L20 Stability and convergence of numerical methods for ordinary differential equations
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