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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.

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.

Suggested Citation

  • Aspandiiarov, S. & Iasnogorodski, R., 1997. "Tails of passage-times and an application to stochastic processes with boundary reflection in wedges," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 115-145, February.
  • Handle: RePEc:eee:spapps:v:66:y:1997:i:1:p:115-145
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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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