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Criterion on stability for Markov processes applied to a model with jumps |
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| Authors: | H. Bessaih R. Kapica T. Szarek |
| Affiliation: | 1. Department of Mathematics, University of Wyoming, Laramie, WY, USA 2. Department of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland 3. Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-952, Gdańsk, Poland |
| Abstract: | We formulate and prove a new criterion for stability of e-processes. In particular we show that any e-process which is averagely bounded and concentrating is asymptotically stable. This general result is applied to a stochastic process with jumps that is a continuous counterpart of the chain considered in Szarek (Ann. Probab. 34:1849–1863, 2006). |
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