The First-Passage Area of Wiener Process with Stochastic Resetting

Mario Abundo ()
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Mario Abundo: Università “Tor Vergata”

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 4, 1-25

Abstract: Abstract For a one-dimensional Wiener process with stochastic resetting $$\mathcal{X}(t)$$ 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 $$X>0,$$ X > 0 , and its first-passage area, that is the random area enclosed between the time axis and the path of the process $$\mathcal{X} (t)$$ 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.

Keywords: First-passage time; First-passage area; Wiener process; Ornstein-Uhlenbeck process; 60J60; 60H05; 60H10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10069-4

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