Stochastic differential equations with reflecting boundary condition in convex regions
Stochastic differential equations with reflecting boundary condition in convex regions
复制标题
DOI：
10.32917/hmj/1206135203
复制
发表时间：
1979
影响因子：
0.2
通讯作者：
Hiroshi Tanaka
中科院分区：
文献类型：
--
作者：
Hiroshi Tanaka
A. V. Skorohod [4]考虑了关于S = [0，oo）的反射扩散过程的随机微分方程（参见McKean [2] [3]）。这是边界条件随机微分方程中最简单的情况，可以很容易地解决。本文的目的是表明，多维版本的Skorohod的方程仍然很容易解决，如果我们假设域D是凸的。描述反射布朗路径的Skorohod方程为
A. V. Skorohod [4] considered a stochastic differential equation for a reflecting diffusion process on 5 = [0, oo) (see also McKean [2] [3]). This is the simplest case among stochastic differential equations subject to boundary conditions and can be solved easily. The purpose of this paper is to show that the multi-dimensional version of Skorohod's equation is still easy to solve if we assume that the domain D is convex. Skorohod's equation describing a reflecting Brownian path ξ on 5 = [0, oo) is