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Some first passage time problems for shot noise processes

Authors:	Jaume Masoliver George H Weiss

Institution:	(1) Department of Chemistry and Institute for Nonlinear Science, University of California, 92093 San Diego, California;(2) Physical Sciences Laboratory, Division of Computer Research and Technology, National Institutes of Health, 20892 Bethesda, Maryland;(3) Present address: Department de Fisica Fonamental, Universitat de Barcelona, 08027 Barcelona, Spain

Abstract:	It has recently been shown that the first passage time problem for a certain class of one-dimensional processes that includes shot noise can be formulated in terms of a set of integral equations. These are found by exact enumeration of all possible trajectories. We show that the equations can be found by more direct means for processes described by the evolution equation $\dot x(t) = f(x) + n(t)$ , wheren(t) is time-localized shot noise.

Keywords:	First passage times shot noise regenerative processes renewal theory
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