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Title: Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem

Abstract

This paper deals with existence and uniqueness of a solution in viscosity sense, for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case is the Hamilton-Jacobi-Bellmann system of the Markovian stochastic optimal m-states switching problem. The switching cost functions depend on (t,x). The main tool is the notion of systems of reflected backward stochastic differential equations with oblique reflection.

Authors:
;  [1]
  1. Universite du Maine, LMM (France)
Publication Date:
OSTI Identifier:
22156414
Resource Type:
Journal Article
Journal Name:
Applied Mathematics and Optimization
Additional Journal Information:
Journal Volume: 67; Journal Issue: 2; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COST; FUNCTIONS; HAMILTON-JACOBI EQUATIONS; MARKOV PROCESS; MATHEMATICAL SOLUTIONS; REFLECTION; VARIATIONAL METHODS; VISCOSITY

Citation Formats

Hamadene, S., E-mail: hamadene@univ-lemans.fr, and Morlais, M. A., E-mail: Marie_Amelie.Morlais@univ-lemans.fr. Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem. United States: N. p., 2013. Web. doi:10.1007/S00245-012-9184-Y.
Hamadene, S., E-mail: hamadene@univ-lemans.fr, & Morlais, M. A., E-mail: Marie_Amelie.Morlais@univ-lemans.fr. Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem. United States. https://doi.org/10.1007/S00245-012-9184-Y
Hamadene, S., E-mail: hamadene@univ-lemans.fr, and Morlais, M. A., E-mail: Marie_Amelie.Morlais@univ-lemans.fr. 2013. "Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem". United States. https://doi.org/10.1007/S00245-012-9184-Y.
@article{osti_22156414,
title = {Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem},
author = {Hamadene, S., E-mail: hamadene@univ-lemans.fr and Morlais, M. A., E-mail: Marie_Amelie.Morlais@univ-lemans.fr},
abstractNote = {This paper deals with existence and uniqueness of a solution in viscosity sense, for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case is the Hamilton-Jacobi-Bellmann system of the Markovian stochastic optimal m-states switching problem. The switching cost functions depend on (t,x). The main tool is the notion of systems of reflected backward stochastic differential equations with oblique reflection.},
doi = {10.1007/S00245-012-9184-Y},
url = {https://www.osti.gov/biblio/22156414}, journal = {Applied Mathematics and Optimization},
issn = {0095-4616},
number = 2,
volume = 67,
place = {United States},
year = {Mon Apr 15 00:00:00 EDT 2013},
month = {Mon Apr 15 00:00:00 EDT 2013}
}