Geodesic
General criteria of integrability of functions of passage-times for non-negative stochastic processes and their applications
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 509-539

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In this paper we study the question of integrability of functions of the first passage-times into compact sets and first return-times for stochastic processes with discrete parameter. We consider first a class of processes with negative drifts taking values in $\mathbb{R}_{+}$ and prove for them general sufficient conditions for integrability of functions of these random times. The conditions are formulated in a martingale spirit initiated by Foster and generalize corresponding results obtained earlier. In the second part of the paper we address a similar question for reflected random walks in a quadrant with zero-drift in the interior. Applying the results of the first part we get conditions for integrability of certain functions of the first passage-times and the first return-times for the reflected random walks. The obtained estimates provide quite sharp results for the former random times and complement the corresponding results in [S. Aspandiiarov and R. Iasnogorodski, Tails of passage-time for non-negative stochastic processes and an application to stochastic processes with boundary reflection in a wedge, Stochastic Process. Appl., 66 (1997), pp. 115–145]. Finally, we derive bounds for the rate of convergence of transition probabilities of ergodic reflected random walks to the corresponding invariant measure.
Keywords: countable Markov chains, recurrence classification, reflected random walks with boundary reflection.
Mots-clés : passage-times 
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     title = {General criteria of integrability of functions of passage-times for non-negative stochastic processes and their applications},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {509--539},
     publisher = {mathdoc},
     volume = {43},
     number = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a5/}
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S. Aspandiiarov; R. Iasnogorodski. General criteria of integrability of functions of passage-times for non-negative stochastic processes and their applications. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 3, pp. 509-539. http://geodesic.mathdoc.fr/item/TVP_1998_43_3_a5/