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The study of diffusion with preferential returns to places visited in the past has attracted an increased attention in recent years. In these highly non-Markov processes, a standard diffusive particle intermittently resets at a given rate…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…
We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…
We analytically investigate the dynamic behavior of an an-isotropic active Brownian particle under various stochastic resetting protocols in two dimensions. The motion of shape-asymmetric active Brownian particles in two dimensions leads to…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
We investigate the role of stochastic resetting in non-Markovian systems, where memory effects arise due to slow relaxation, rugged energy landscapes, disordered environments, and molecular crowding. Using the celebrated continuous-time…
The constructive role of non-Gaussian random fluctuations is studied in the context of the passage over the dichotomously switching potential barrier. Our attention focuses on the interplay of the effects of independent sources of…
We study the dynamics of symmetric exclusion process (SEP) in the presence of stochastic resetting to two possible specific configurations -- with rate $r_1$ (respectively, $r_2$) the system is reset to a step-like configuration where all…
We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the non-equilibrium stationary state…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a non-monotonic behavior of the frequency dependent first passage time probability density…
We consider the mean first passage time (MFPT) for a diffusive particle in a potential landscape with the extra condition that the particle is reset to its original position with some rate r. We study non-smooth and non-convex potentials…
Given a one-dimensional stochastic differential equation, one can associate to this equation a stochastic flow on $[0,+\infty )$, which has an absorbing barrier at zero. Then one can define its dual stochastic flow. In \cite{AW}, Akahori…
We present a method for enhanced sampling of molecular dynamics simulations using stochastic resetting. Various phenomena, ranging from crystal nucleation to protein folding, occur on timescales that are unreachable in standard simulations.…
We discuss how to exploit stochastic resonance with the methods of statistical theory of decisions. To do so, we evaluate two detection strategies: escape time analysis and strobing. For a standard quartic bistable system with a periodic…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
A space fractional diffusion-like equation is introduced, which embodies the nonlocality in time, represented by the memory kernel and the non-locality in space. A specific example of the nonlocal term is considered in combination with…
We study stochastic resetting of a probe particle in a viscoelastic environment where only the probe is reset while the medium retains memory of its past dynamics. Using a minimal model with finite correlation time, we analyze the…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…