J. Villarroel Rodriguez
We consider a continuous-time Brownian motion in one space dimension regenerated according to an independent Poisson process. At the Poisson epochs, the resulting system is restarted to the initial position to start anew, in such a way that the ensuing evolution is independent of the past. We describe the probability that starting from 0 the Brownian particle escapes the interval (a,b)--where a<0<b-- via the upper barrier b. We then study the distribution of the escape time and optimal reset mechanisms appropriate to search problems, which minimize the hitting time. In the last part, we use the Girsanov-Radon-Nikodym theorem to study the effect of the incorporation of a drift.
Palabras clave: Brownian motion,regeneration process, Poisson process
Programado
GT17 Procesos Estocásticos y sus Aplicaciones III
7 de junio de 2022 16:50
A26
