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An adaptive Euler-Maruyama scheme for SDDEs by Liu, Dongyang; Song, Minghui; Zhang, Yuhang is a scholarly article available to read on EtoBox.

What is An adaptive Euler-Maruyama scheme for SDDEs about?

This paper proposes an adaptive numerical method for stochastic delay differential equations (SDDEs) with a non-global Lipschitz drift term and a non-constant delay, building upon the work of Wei Fang and others. The method adapts the step size based on the growth of the drift term. Differing slightly from the conventional Euler-Maruyama format, this paper addresses the estimation of the delay term by substituting it with the numerically obtained solution closest to the left endpoint.This approach overcomes the challenge of numerical nodes not falling within the nodes after subtracting the delay. The paper proves the convergence of the numerical method for a class of non-global Lipschitz continuous SDDEs under the assumption that the step size function satisfies certain conditions.

Author

Liu, Dongyang; Song, Minghui; Zhang, Yuhang

Published

2024

Language

EN