Existence and Uniqueness of Semimartingale Reflecting Brownian Motions in Convex Polyhedrons
- 1 January 1996
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in Theory of Probability and Its Applications
- Vol. 40 (1) , 1-40
- https://doi.org/10.1137/1140001
Abstract
We consider the problem of existence and uniqueness of semimartingale reflecting Brownian motions(SRBM's) in convex polyhedrons. Loosely speaking, such a process has a semimartingaledecomposition such that in the interior of the polyhedron the process behaves like a Brownianmotion with a constant drift and covariance matrix, and at each of the (d \Gamma 1)-dimensionalfaces that form the boundary of the polyhedron, the bounded variation part of the processincreases in a given direction...Keywords
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