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 such that the dynamicsis renewed intermittently. Quite surprisingly , although resetting renders GBM stationary, the resulting process remains non-ergodic. We observe three different long-time regimes: a quenched state, an unstable and a stable annealed state depending on the resetting strength.  Crucially, the  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.
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.
R
such that the dynamicsis renewed intermittently. Quite surprisingly
, which consecutively renews its dynamics. We show that
R
We
Quite surprisingly, the effect of resetting is pivotal in manifesting the non-ergodic behavior. In particular, we
A
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.
A
above-mentioned