Convex duality and the Skorokhod Problem. II |
| |
Authors: | Paul Dupuis Kavita Ramanan |
| |
Institution: | (1) Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, RI 02912, USA (e-mail: dupuis@cfm.brown.edu), US;(2) Bell Laboratories, Lucent Technologies, 600 Mountain Avenue, Murray Hill, New Jersey 07974, USA (e-mail: kavita@research.bell-labs.com), US |
| |
Abstract: | In this paper we consider Skorokhod Problems on polyhedral domains with a constant and possibly oblique constraint direction
specified on each face of the domain, and with a corresponding cone of constraint directions at the intersection of faces.
In part one of this paper we used convex duality to develop new methods for the construction of solutions to such Skorokhod
Problems, and for proving Lipschitz continuity of the associated Skorokhod Maps. The main alternative approach to Skorokhod
Problems of this type is the reflection mapping technique introduced by Harrison and Reiman 8]. In this part of the paper
we apply the theory developed in part one to show that the reflection mapping technique of 8] is restricted to a slight generalization
of the class of problems originally considered in 8]. We further illustrate the power of the duality approach by applying
it to two other classes of Skorokhod Problems – those with normal directions of constraint, and a new class that arises from
a model of processor sharing in communication networks. In particular, we prove existence of solutions to and Lipschitz continuity
of the Skorokhod Maps associated with each of these Skorokhod Problems.
Received: 17 April 1998 / Revised: 8 January 1999 |
| |
Keywords: | Mathematics Subject Classification (1991): 34A60 52B11 60K25 60G99 93A30 |
本文献已被 SpringerLink 等数据库收录! |
|