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Optimal Control of JumpMarkov Processes and Viscosity Solutions
 Halil Mete Soner
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Abstract
We investigate the Bellman equation that arises in the optimal control of Markov processes. This is a fully nonlinear integrodifferential equation. The notion of viscosity solutions is introduced and then existence and uniqueness results are obtained. Also, the connection between the optimal control problem and the Bellman equation is developed.
This research was supported in part by the Institute for Mathematics and its Applications with funds provided by the National Science Foundation and the Office of Naval Research.
This research was completed while the author was visiting the Institute for Mathematics and its Applications.
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 Title
 Optimal Control of JumpMarkov Processes and Viscosity Solutions
 Book Title
 Stochastic Differential Systems, Stochastic Control Theory and Applications
 Pages
 pp 501511
 Copyright
 1988
 DOI
 10.1007/9781461387626_29
 Print ISBN
 9781461387640
 Online ISBN
 9781461387626
 Series Title
 The IMA Volumes in Mathematics and Its Applications
 Series Volume
 10
 Series ISSN
 09406573
 Publisher
 Springer New York
 Copyright Holder
 SpringerVerlag New York
 Additional Links
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 Editors

 Wendell Fleming ^{(1)}
 PierreLouis Lions ^{(2)}
 Editor Affiliations

 1. Division of Applied Mathematics, Brown University
 2. Ceremade, Universite ParisDauphine
 Authors

 Halil Mete Soner ^{(3)}
 Author Affiliations

 3. Deparment of Mathematics, CarnegieMellon University, Schenley Park, Pittsburgh, PA, 15213, USA
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