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Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first arrival time (MFAT) to a given position $x$, may reach it in a finite time when they reset their position. In this work we study these emerging phenomena from a unified perspective. On one hand we study the existence of a finite equilibrium MSD when resets are applied to random motion with $langle x^2(t)rangle _msim t^p$ for $0<pleq2$. For exponentially distributed reset times, a compact formula is derived for the equilibrium MSD of the overall process in terms of the mean reset time and the motion MSD. On the other hand, we also test the robustness of the finiteness of the MFAT for different motion dynamics which are subject to stochastic resets. Finally, we study a biased Brownian oscillator with resets with the general formulas derived in this work, finding its equilibrium first moment and MSD, and its MFAT to the minimum of the harmonic potential.
In this work we consider a stochastic movement process with random resets to the origin followed by a random residence time there before the walker restarts its motion. First, we study the transport properties of the walker, we derive an expression f
Random walks with stochastic resetting provides a treatable framework to study interesting features about central-place motion. In this work, we introduce non-instantaneous resetting as a two-state model being a combination of an exploring state wher
A hot Markovian system can cool down faster than a colder one: this is known as the Mpemba effect. Here, we show that a non-equilibrium driving via stochastic reset can induce this phenomenon, when absent. Moreover, we derive an optimal driving proto
We study a stochastic process $X_t$ related to the Bessel and the Rayleigh processes, with various applications in physics, chemistry, biology, economics, finance and other fields. The stochastic differential equation is $dX_t = (nD/X_t) dt + sqrt{2D
Explicit expressions for arrival times of particles moving in a one-dimensional Zero-Range Process (ZRP) are computed. Particles are fed into the ZRP from an injection site and can also evaporate from anywhere in the interior of the ZRP. Two dynamics