Tails of passage-times and an application to stochastic processes with boundary reflection in wedges
AbstractIn 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 InfoArticle provided by Elsevier in its journal Stochastic Processes and their Applications.
Volume (Year): 66 (1997)
Issue (Month): 1 (February)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description
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- 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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