Random acceleration process under stochastic resetting

Characterization of stationary states in random walks with stochastic resetting.

It is known that introducing a stochastic resetting in a random-walk process can lead to the emergence of a stationary state. Here we study this point from a general perspective through the derivation and analysis of mesoscopic (continuous-time random walk) equations for both jump and velocity models with stochastic resetting. In the case of jump models it is shown that stationary states emerge...

Diffusion with stochastic resetting.

We study simple diffusion where a particle stochastically resets to its initial position at a constant rate r. A finite resetting rate leads to a nonequilibrium stationary state with non-Gaussian fluctuations for the particle position. We also show that the mean time to find a stationary target by a diffusive searcher is finite and has a minimum value at an optimal resetting rate r*. Resetting ...

Stochastic Learning under Random Reshuffling

In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works have pursued justifications for this behavior by examining the convergence rate of the learning process under diminishing step-sizes. This work focuses on t...

Stochastic Acceleration in an Inhomogenous Time Random Force Field

This paper studies the asymptotic behavior of a particle with large initial velocity and subject to a force field which is randomly time dependent and inhomogenous in space. We analyze the diffusive limit ǫ → 0 of the position–velocity pair under the appropriate space-time rescaling: ( ǫY (s/ǫ), ǫẎ (s/ǫ) ) . Two alternative approaches are proposed. The first one is based on hydrodynamic limits ...

Random Process Simulation for Stochastic Fatigue Analysis