First-passage Brownian functionals with stochastic resetting
Prashant Singh,
Arnab Pal
Abstract:We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A firstpassage functional is defined aswhere t f is the first-passage time of a reset Brownian process x(τ ), i.e., the first time the process crosses zero. In here, the particle is reset to x R > 0 at a constant rate r starting from x 0 > 0 and we focus on the following functionals:, and (iii) functionals of the form A n = ´tf 0 dτ [x(τ )] n with n > −2. For first… Show more
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