Work

Distributional and Extremal Behaviour of Brownian Motion with Exponential Resetting

Year: 2026

Type: article

Abstract: We study the distributional and asymptotic properties of the supremum of Brownian motion with drift and exponential resetting. We obtain an explicit renewal-type formula for the distribution of the supremum and then derive an approximation for its survival function. Moreover, we find the asymptotics of the tail distribution of the supremum and infimum. We also consider the stationary case and give a new explicit expression for the two-dimensional distributions of such processes.

Source: Methodology And Computing In Applied Probability

DOI: 10.1007/s11009-026-10316-4

Authors: Krzysztof Dȩbicki, Enkelejd Hashorva, Zbigniew Michna

Institutions: University of Wrocław, University of Lausanne, Wrocław University of Science and Technology

Language: English

Topic: Probability and Risk Models

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Narodowe Centrum Nauki, Narodowym Centrum Nauki