Speaker
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.
