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We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…

Probability · Mathematics 2007-05-23 Samuel Herrmann , Peter Imkeller , Dierk Peithmann

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…

Risk Management · Quantitative Finance 2021-08-24 Viktor Stojkoski , Trifce Sandev , Ljupco Kocarev , Arnab Pal

We propose a random adaptation variant of time-varying distributed averaging dynamics in discrete time. We show that this leads to novel interpretations of fundamental concepts in distributed averaging, opinion dynamics, and distributed…

Optimization and Control · Mathematics 2022-06-28 Rohit Parasnis , Ashwin Verma , Massimo Franceschetti , Behrouz Touri

We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…

Statistical Mechanics · Physics 2021-07-16 M. Reza Shaebani , Heiko Rieger

We explore the effect of stochastic resetting on the first-passage properties of Feller process. The Feller process can be envisioned as space-dependent diffusion, with diffusion coefficient $D(x)=x$, in a potential…

Statistical Mechanics · Physics 2022-09-27 Somrita Ray

The random arrest of the diffusion of a single particle and its return to its origin has served as the paradigmatic example of a large variety of processes undergoing stochastic resetting. While the implications and applications of…

Soft Condensed Matter · Physics 2025-04-15 Ron Vatash , Yael Roichman

We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…

Statistical Mechanics · Physics 2023-07-07 M. Reza Shaebani , Heiko Rieger , Zeinab Sadjadi

Understanding the stochastic properties of conductance fluctuations in disordered mesoscopic systems is fundamental to quantum transport. In this work, we investigate the multifractal and ergodic properties of the fictitious time series of…

The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…

Dynamical Systems · Mathematics 2009-11-13 Xinghua Deng , Robert V. Moody

The main objective of this paper is to study the time decay of transport-diffusion equation with inhomogeneous localized damping in the multi-dimensional torus. The drift is governed by an autonomous Lipschitz vector field and the diffusion…

Analysis of PDEs · Mathematics 2020-04-17 Kaïs Ammari , Taoufik Hmidi

We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the…

Returning a system to a desired state under a force field involves a thermodynamic cost, i.e., {\it work}. This cost fluctuates for a small-scale system from one experimental realization to another. We introduce a general framework to…

Statistical Mechanics · Physics 2022-12-07 Deepak Gupta , Carlos A. Plata

We look into the problem of stochastic resetting with refractory periods. The model dynamics comprises diffusive and motionless phases. The diffusive phase ends at random time instants, at which the system is reset to a given position --…

Statistical Mechanics · Physics 2024-03-26 Gregorio García-Valladares , Deepak Gupta , Antonio Prados , Carlos A. Plata

A subthreshold signal is transmitted through a channel and may be detected when some noise -- with known structure and proportional to some level -- is added to the data. There is an optimal noise level, called stochastic resonance, that…

Statistics Theory · Mathematics 2007-06-13 Stefano M. Iacus

In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied…

Statistical Mechanics · Physics 2019-10-23 Axel Masó-Puigdellosas , Daniel Campos , Vicenç Méndez

Stochastic resetting is known for its ability to accelerate search processes and induce non-equilibrium steady states. Here, we compare the relaxation times and resulting steady states of resetting and thermal relaxation for Brownian motion…

Statistical Mechanics · Physics 2025-10-31 Nir Sherf , Remi Goerlich , Barak Hirshberg , Yael Roichman

This paper deals with some self-interacting diffusions $(X_t,t\geq 0)$ living on $\mathbb{R}^d$. These diffusions are solutions to stochastic differential equations: \[\mathrm{d}X_t=\mathrm{d}B_t-g(t)\nabla…

Probability · Mathematics 2012-01-05 Sébastien Chambeu , Aline Kurtzmann

The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study…

Statistical Mechanics · Physics 2011-12-13 Adrian A. Budini

In branching diffusions with immigration (BDI), particles travel on independent diffusion paths in $\mathbb{R}^d$, branch at position-dependent rates and leave offspring -- randomly scattered around the parent's death position -- according…

Probability · Mathematics 2019-05-08 Matthias Hammer , Reinhard Höpfner , Tobias Berg

We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form $D(x)\sim D_0|x|^\alpha$ in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the…

Statistical Mechanics · Physics 2015-06-23 Andrey G. Cherstvy , Ralf Metzler