The first-passage area of Wiener process with stochastic resetting. (English) Zbl 07826461
The article considers a scalar brownian motion reset to a fixed state at a specified rate. Using Laplace transform techniques, individual and joint moments of its first passage time through zero and area under its trajectory till the first passage time are computed, and the distribution function of its maximum displacement is derived. The results are then extended to a brownian motion with constant drift and reset.
Reviewer: Vivek S. Borkar (Mumbai)
Keywords:
brownian motion with reset; first passage time; first passage area; maximum displacement; brownian motion with a drift and resetReferences:
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