کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4640153 | 1341263 | 2011 | 13 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: An application of Taylor series in the approximation of solutions to stochastic differential equations with time-dependent delay An application of Taylor series in the approximation of solutions to stochastic differential equations with time-dependent delay](/preview/png/4640153.png)
The subject of this paper is the analytic approximation method for solving stochastic differential equations with time-dependent delay. Approximate equations are defined on equidistant partitions of the time interval, and their coefficients are Taylor approximations of the coefficients of the initial equation. It will be shown, without making any restrictive assumption for the delay function, that the approximate solutions converge in LpLp-norm and with probability 1 to the solution of the initial equation. Also, the rate of the LpLp convergence increases when the degrees in the Taylor approximations increase, analogously to what is found in real analysis. At the end, a procedure will be presented which allows the application of this method, with the assumption of continuity of the delay function.
Journal: Journal of Computational and Applied Mathematics - Volume 235, Issue 15, 1 June 2011, Pages 4439–4451