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.
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Abundo, M. (2007). On First-Passage Problems for Asymmetric One-Dimensional Diffusions. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2007. EUROCAST 2007. Lecture Notes in Computer Science, vol 4739. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75867-9_23
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DOI: https://doi.org/10.1007/978-3-540-75867-9_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75866-2
Online ISBN: 978-3-540-75867-9
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