A1432
Title: Distributional and extremal behaviour of Brownian motion with exponential resetting
Authors: Krzysztof Debicki - University of Wroclaw (Poland)
Enkelejd Hashorva - University of Lausanne (Switzerland)
Zbigniew Michna - Wroclaw University of Science and Technology (Poland) [presenting]
Abstract: The distributional and asymptotic properties of the supremum of Brownian motion with drift and exponential resetting are studied. An explicit renewal-type formula for the distribution of the supremum is obtained, and an approximation for its survival function is derived. The asymptotics of the tail distribution of the supremum and infimum are determined. Additionally, the stationary case is considered and a new explicit expression for the two-dimensional distributions of such processes is provided.
