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Stability of linear stochastic difference equations in strategically controlled random environments

Part of: Stochastic systems and control Game theory Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Ulrich Horst
Ulrich Horst*
Affiliation:
Humboldt-Universität zu Berlin
*
∗ Postal address: Institut für Mathematik, Bereich Stochastik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany. Email address: horst@mathematik.hu-berlin.de
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Abstract

We consider the stochastic sequence {Yt}t∈ℕ defined recursively by the linear relation Yt+1=AtYt+Bt in a random environment. The environment is described by the stochastic process {(At,Bt)}t∈ℕ and is under the simultaneous control of several agents playing a discounted stochastic game. We formulate sufficient conditions on the game which ensure the existence of Nash equilibria in Markov strategies which have the additional property that, in equilibrium, the process {Yt}t∈ℕ converges in distribution to a stationary regime.

Keywords

Stochastic difference equationstochastic stabilitystochastic gamesrandom systems with complete connections

MSC classification

Primary: 60G35: Signal detection and filtering 93E15: Stochastic stability 91A15: Stochastic games
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 961 - 981
Copyright
Copyright © Applied Probability Trust 2003 

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