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Tails of passage-times and an application to stochastic processes with boundary reflection in wedges

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  • Aspandiiarov, S.
  • Iasnogorodski, R.
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    Abstract

    In this paper we obtain lower bounds for the tails of the distributions of the first passage-times for some stochastic processes. We consider first discrete parameter processes with asymptotically small drifts taking values in + and prove for them a general result giving lower bounds for these tails. As an application of the obtained results, we obtain lower bounds for the tails of the distributions of the first passage-times for reflected random walks in a quadrant with zero-drift in the interior. The latter bounds are then used to get explicit conditions for the finiteness or not of the moments of the first passage-time to the origin for a Brownian motion with oblique reflection in a wedge.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 66 (1997)
    Issue (Month): 1 (February)
    Pages: 115-145

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    Handle: RePEc:eee:spapps:v:66:y:1997:i:1:p:115-145

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    Related research

    Keywords: Passage-times Recurrence classification Markov chain with boundary reflection Reflected Brownian motion;

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    Cited by:
    1. Hryniv, Ostap & Menshikov, Mikhail V. & Wade, Andrew R., 2013. "Excursions and path functionals for stochastic processes with asymptotically zero drifts," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 1891-1921.

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