The first-passage area of Wiener process with stochastic resetting

2023/06/21 by Mario Abundo, Abundo, Mario · 2 citations
Biochemistry, Genetics and Molecular Biology · #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2306.12154

openalex publication_date 2023/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Optimization in the first-passage problem of a diffusion with Poissonian resetting
• Queueing models with random resetting

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• Limit theorems for the Wiener process with resetting
• Inverse first-passage problems of a diffusion with resetting
• First-passage time of a Brownian searcher with stochastic resetting to random positions
• Optimization in the first-passage problem of a diffusion with Poissonian resetting
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