A randomized first-passage problem for drifted Brownian motion subject to hold and jump from a boundary
Abstract
We study an inverse first-passage-time problem for Wiener process X(t) subject to hold and jump from a boundary c. Let be given a threshold S>X(0) c, and a distribution function F on [0, + ∞ ). The problem consists in finding the distribution of the holding time at c and the distribution of jumps from c, so that the first-passage time of X(t) through S has distribution F.
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