On stochastic solutions of nonlocal random functional integral equations

Q2 Mathematics
M.M. Elborai , M.I. Youssef
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引用次数: 5

Abstract

In this paper, we use Schauder’s fixed point to establish the existence of at least one solution for a functional nonlocal stochastic differential equation under sufficient conditions in the space of all square integrable stochastic processes with a finite second moment. We state and prove the conditions which guarantee the uniqueness of the solution. We solve a nonlinear example analytically and obtain the initial condition which makes the solution passes through a random position with a given normal distribution at a specified time. Also, the Milstein scheme to this example is studied.

非局部随机泛函积分方程的随机解
利用Schauder不动点,在有限二阶矩的所有平方可积随机过程空间中,证明了一类泛函非局部随机微分方程在充分条件下至少有一个解的存在性。我们陈述并证明了保证解的唯一性的条件。本文对一个非线性实例进行了解析求解,得到了使解在给定时间内经过具有给定正态分布的随机位置的初始条件。此外,本文还研究了该实例的Milstein格式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Arab Journal of Mathematical Sciences
Arab Journal of Mathematical Sciences Mathematics-Mathematics (all)
CiteScore
1.20
自引率
0.00%
发文量
17
审稿时长
8 weeks
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