Stability Analysis of Numerical Schemes for Stochastic Differential Equations
- 1 December 1996
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 33 (6), 2254-2267
- https://doi.org/10.1137/s0036142992228409
Abstract
Stochastic differential equations (SDEs) represent physical phenomena dominated by stochastic processes. As for deterministic ordinary differential equations (ODEs), various numerical schemes are proposed for SDEs. In this paper we study the stability of numerical schemes for scalar SDEs with respect to the mean-square norm, which we call $MS$-stability. We will show some figures of the $MS$-stability domain or regions for some numerical schemes and present numerical results which confirm it. This notion is an extension of absolute stability in numerical methods for ODEs.This publication has 17 references indexed in Scilit:
- A-stability of Runge-Kutta methods for systems with additive noiseBIT Numerical Mathematics, 1992
- Numerical Solution of Stochastic Differential EquationsPublished by Springer Science and Business Media LLC ,1992
- Higher-order implicit strong numerical schemes for stochastic differential equationsJournal of Statistical Physics, 1992
- THE NUMERICAL SOLUTION OF NONLINEAR STOCHASTIC DYNAMICAL SYSTEMS: A BRIEF INTRODUCTIONInternational Journal of Bifurcation and Chaos, 1991
- A survey of numerical methods for stochastic differential equationsStochastic Environmental Research and Risk Assessment, 1989
- Simulation studies on time discrete diffusion approximationsMathematics and Computers in Simulation, 1987
- Numerical Integration of Multiplicative-Noise Stochastic Differential EquationsSIAM Journal on Numerical Analysis, 1985
- Approximate Integration of Stochastic Differential EquationsTheory of Probability and Its Applications, 1975
- Generalized Cumulant Expansion MethodJournal of the Physics Society Japan, 1962
- Continuous Markov processes and stochastic equationsRendiconti del Circolo Matematico di Palermo Series 2, 1955