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Stability of linear stochastic difference equations in strategically controlled random environments

Published online by Cambridge University Press:  01 July 2016

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: [email protected]

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.

Type
General Applied Probability
Copyright
Copyright © Applied Probability Trust 2003 

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