The Skorokhod Oblique Reflection Problem in a Convex Polyhedron
نویسنده
چکیده
The Skorokhod oblique reflection problem is studied in the case of n-dimensional convex polyhedral domains. The natural sufficient condition on the reflection directions is found, which together with the Lipschitz condition on the coefficients gives the existence and uniqueness of the solution. The continuity of the corresponding solution mapping is established. This property enables one to construct in a direct way the reflected (in a convex polyhedral domain) diffusion processes possessing the nice properties.
منابع مشابه
Convex Duality and the Skorokhod Problem
The solution to the Skorokhod Problem de nes a deterministic mapping, referred to as the Skorokhod Map, that takes unconstrained paths to paths that are con ned to live within a given domainG IRn. Given a set of allowed constraint directions for each point of @G, the solution to the Skorokhod Problem de nes the constrained version of , where the constraining force acts along one of the given bo...
متن کاملAn invariance principle for semimartingale reflecting Brownian motions in domains with piecewise smooth boundaries
Semimartingale reflecting Brownian motions (SRBMs) living in the closures of domains with piecewise smooth boundaries are of interest in applied probability because of their role as heavy traffic approximations for some stochastic networks. In this paper, assuming certain conditions on the domains and directions of reflection, a perturbation result, or invariance principle, for SRBMs is proved....
متن کاملABCD matrix for reflection and refraction of laser beam at tilted concave and convex elliptic paraboloid interfaces and studying laser beam reflection from a tilted concave parabola of revolution
Studying Gaussian beam is a method to investigate laser beam propagation and ABCD matrix is a fast and simple method to simulate Gaussian beam propagation in different mediums. Of the ABCD matrices studied so far, reflection and refraction matrices at various surfaces have attracted a lot of researches. However in previous work the incident beam and the principle axis of surface are in parallel...
متن کاملAn Invariance Principle for Semimartingale Reflecting Brownian Motions in Domains with Piecewise Smooth Boundaries1 by W. Kang
Semimartingale reflecting Brownian motions (SRBMs) living in the closures of domains with piecewise smooth boundaries are of interest in applied probability because of their role as heavy traffic approximations for some stochastic networks. In this paper, assuming certain conditions on the domains and directions of reflection, a perturbation result, or invariance principle, for SRBMs is proved....
متن کاملReflected Diffusions Defined via the Extended Skorokhod Map
This work introduces the extended Skorokhod problem (ESP) and associated extended Skorokhod map (ESM) that enable a pathwise construction of reflected diffusions that are not necessarily semimartingales. Roughly speaking, given the closure G of an open connected set in R , a non-empty convex cone d(x) ⊂ R specified at each point x on the boundary ∂G, and a càdlàg trajectory ψ taking values in R...
متن کامل