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Limit theorems for stochastically perturbed dynamical systems

Published online by Cambridge University Press:  14 July 2016

Krzysztof Łoskot*
Affiliation:
Silesian University, Katowice
Ryszard Rudnicki*
Affiliation:
Polish Academy of Sciences, Katowice
*
Postal address: Institute of Mathematics, Silesian University, 40–007 Katowice, Poland.
∗∗Postal adress: Institute of Mathematics, Polish Academy of Sciences, Staromiejska 8/6, 40–013 Katowice, Poland.

Abstract

We consider a discrete-time stochastically perturbed dynamical system on the Polish space given by the recurrence formula Xn = S(Xn–1, Yn), where Yn are i.i.d. random elements. We prove the existence of unique stationary measure and versions of classical limit theorems for the process (Xn).

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Research supported by the State Committee for Scientific Research Grant No. 2 P301 026 05.

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