Introduction to the numerical analysis of stochastic delay differential equations

[摘要] We consider the problem of the numerical solution of stochastic delay differential equations of Ito form dX(t) = f(X(t),X(t - tau))dt + g(X(t),X(t - tau))dW(t), t is an element of [0,T] and X(t) = Psi (t) for t is an element of [ -tau ,0], with given f,g, Wiener noise W and given tau > 0, with a prescribed initial function Psi. We indicate the nature of the equations of interest and give a convergence proof for explicit single-step methods. Some illustrative numerical examples using a strong Euler-Maruyama scheme are provided. (C) 2000 Elsevier Science B.V. All rights reserved.

[发布日期] 2000-12-15