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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.

MSC:
60H10Stochastic ordinary differential equations
65C99Probabilistic methods, simulation and stochastic differential equations (numerical analysis)
65C20Models (numerical methods)
65L20Stability and convergence of numerical methods for ODE