首页|Convergence and stability of stochastic theta method for nonlinear stochastic differential equations with piecewise continuous arguments
Convergence and stability of stochastic theta method for nonlinear stochastic differential equations with piecewise continuous arguments
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NSTL
Elsevier
This paper deals with the strong convergence and exponential stability of the stochastic theta (ST) method for stochastic differential equations with piecewise continuous arguments (SDEPCAs) with non-Lipschitzian and non-linear coefficients and mainly includes the following three results: (i) under the local Lipschitz and the monotone conditions, the ST method with theta is an element of [1/2, 1] is strongly convergent to SDEPCAs; (ii) the ST method with theta is an element of (1/2, 1] preserves the exponential mean square stability of SDEPCAs under the monotone condition and some conditions on the step-size; (iii) without any restriction on the step-size, there exists theta* is an element of (1/2, 1] such that the ST method with theta is an element of (theta*, 1] is exponentially stable in mean square. Moreover, for sufficiently small step-size, the rate constant can be reproduced. Some numerical simulations are provided to illustrate the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
Stochastic differential equations with piecewise continuous argumentsSuper-linear growthThe stochastic theta (ST) methodConvergence of the ST methodExponential mean square stabilityBACKWARD EULERTIMESTABILIZATIONRATES
NSTL
Elsevier
