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Limit theorems for stochastically perturbed dynamical systems

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Krzysztof Łoskot  and
Ryszard Rudnicki
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.
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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).

Keywords

INVARIANT MEASURELIMIT THEOREMS

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces
Secondary: 60F05: Central limit and other weak theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 2 , June 1995 , pp. 459 - 469
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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