Arcsine laws for Brownian motion with Poissonian resetting
Kacper Ta\'zbierski, Marcin Magdziarz
TL;DR
This paper extends classical arcsine laws to Brownian motion with Poissonian resetting, providing explicit formulas for the first two laws and numerical insights for the third, enhancing understanding of stochastic processes with resets.
Contribution
It introduces the first explicit formulas for arcsine laws under Poissonian resetting, a novel extension of classical stochastic process results.
Findings
Closed-form formulas for the first and second arcsine laws with resetting
Numerical results for the third arcsine law
Enhanced understanding of Brownian motion with resets
Abstract
We analyze the equivalents of the celebrated arcsine laws for Brownian motion undergoing Poissonian resetting. We obtain closed-form formulae for the probability density functions of the corresponding random variables in the cases of the first and second arcsine law. Furthermore, we obtain numerical results for the third law.
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Taxonomy
TopicsDiffusion and Search Dynamics · Micro and Nano Robotics