Stability of linear stochastic difference equations in strategically controlled random environments
Ulrich Horst
Source: Adv. in Appl. Probab. Volume 35, Number 4
(2003), 961-981.
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.
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Keywords: Stochastic difference equation; stochastic stability; stochastic games; random systems with complete connections
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aap/1067436330
Digital Object Identifier: doi:10.1239/aap/1067436330
Mathematical Reviews number (MathSciNet): MR2014265
Zentralblatt MATH identifier: 02052108
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