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The first-passage area of Wiener process with stochastic resetting
Mario Abundo · 2023-06-21 · via math.PR updates on arXiv.org

For a one-dimensional Wiener process with stochastic resetting ${\cal X}(t)$, obtained from an underlying Wiener process $X(t),$ we study the statistical properties of its first-passage time through zero, when starting from $x>0,$ and its first-passage area, that is the random area enclosed between the time axis and the path of the process ${\cal X} (t)$ up to the first-passage time through zero. By making use of solutions of certain associated ODEs, we are able to find explicit expressions for the Laplace transforms of the first-passage time and the first-passage area, and their single and joint moments.

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