27–29 Sept 2021
Online
Europe/Warsaw timezone
Abstract submission and Registration are closed.

Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process

28 Sept 2021, 16:30
20m
Online

Online

Contributed talk S6

Speaker

Viktor Stojkoski (Macedonian Academy of Sciences and Arts)

Description

We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical
stochastic multiplicative process for non-stationary and non-ergodic dynamics. Resetting is a sudden
interruption of a process, which consecutively renews its dynamics. We show that, although resetting
renders GBM stationary, the resulting process remains non-ergodic. Quite surprisingly, the effect
of resetting is pivotal in manifesting the non-ergodic behavior. In particular, we observe three
different long-time regimes: a quenched state, an unstable and a stable annealed state depending
on the resetting strength. Notably, in the last regime, the system is self-averaging and thus the
sample average will always mimic ergodic behavior establishing a stand alone feature for GBM
under resetting. Crucially, the above-mentioned regimes are well separated by a self-averaging time
period which can be minimized by an optimal resetting rate. Our results can be useful to interpret
data emanating from stock market collapse or reconstitution of investment portfolios.

Primary author

Viktor Stojkoski (Macedonian Academy of Sciences and Arts)

Co-authors

Dr Trifce Sandev (Macedonian Academy of Sciences and Arts, Skopje, Macedonia) Dr Arnab Pal (Indian Institute of Technology Kanpur) Dr Ljupco Kocarev (Macedonian Academy of Sciences and Arts)

Presentation materials

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