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On First-Passage Problems for Asymmetric One-Dimensional Diffusions

  • Mario Abundo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4739)

Abstract

For a,b > 0, we consider a temporally homogeneous, one-dimensional diffusion process X(t) defined over I = ( − b, a), with infinitesimal parameters depending on the sign of X(t). We suppose that, when X(t) reaches the position 0, it is reflected rightward to δ with probability p > 0 and leftward to − δ with probability 1 − p, where δ> 0. It is presented a method to find approximate formulae for the mean exit time from the interval ( − b,a), and for the probability of exit through the right end a, generalizing the results of Lefebvre ([1]) holding, in the limit δ→0, for asymmetric Brownian motion with drift.

Keywords

Asymmetric diffusion Brownian motion First-exit time 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Mario Abundo
    • 1
  1. 1.Dipartimento di Matematica, Università Tor Vergata, 00133 RomaItaly

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