English
Related papers

Related papers: An intermediate regime for exit phenomena driven b…

200 papers

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises,…

Statistical Mechanics · Physics 2009-11-13 B. Dybiec , E. Gudowska-Nowak , I. M. Sokolov

Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…

Dynamical Systems · Mathematics 2013-06-04 Ting Gao , Jinqiao Duan

L\'evy noise influences diverse non-equilibrium systems across scales, including quantum devices, active biological matter, and financial markets. While such noise is pervasive, its overall impact on activated transitions between metastable…

Statistical Mechanics · Physics 2025-11-25 Shenglan Yuan

It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the investigation of nonlinear phenomena whose mathematical models…

Probability · Mathematics 2020-08-21 Yubin Lu , Jinqiao Duan

The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian L\'evy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian…

Statistics Theory · Mathematics 2020-07-15 Yang Li , Jinqiao Duan , Xianbin Liu , Yanxia Zhang

We find analytical solution of pair of stochastic equations with arbitrary forces and multiplicative L\'evy noises in a steady-state nonequilibrium case. This solution shows that L\'evy flights suppress always a quasi-periodical motion…

Statistical Mechanics · Physics 2010-01-04 A. I. Olemskoi , S. S. Borysov , I. A. Shuda

We use the mean exit time to quantify macroscopic dynamical behaviors of stochastic dynamical systems driven by tempered L\'evy fluctuations, which are solutions of nonlocal elliptic equations. Firstly, we construct a new numerical scheme…

Dynamical Systems · Mathematics 2019-10-22 Yanjie Zhang , Xiao Wang , Jinqiao Duan

We consider a dynamical system described by the differential equation $\dot{Y}_t=-U'(Y_t)$ with a unique stable point at the origin. We perturb the system by the L\'evy noise of intensity $\varepsilon$ to obtain the stochastic differential…

Probability · Mathematics 2009-06-10 Peter Imkeller , Ilya Pavlyukevich , Torsten Wetzel

We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by L\'evy stable noises. The complexity of the first passage time statistics (mean first passage time,…

Statistical Mechanics · Physics 2020-03-16 B. Dybiec , E. Gudowska-Nowak , P. Hänggi

Effects of non-Gaussian $\alpha-$stable L\'evy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density from inside a safe or benign domain. The mean exit…

Dynamical Systems · Mathematics 2016-12-21 Jian Ren , Chujin Li , Ting Gao , Xingye Kan , Jinqiao Duan

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When…

chao-dyn · Physics 2008-02-03 Robert S. Maier , D. L. Stein

Phase transitions and effects of external noise on many body systems are one of the main topics in physics. In mean field coupled nonlinear dynamical stochastic systems driven by Brownian noise, various types of phase transitions including…

Statistical Mechanics · Physics 2015-05-13 Akihisa Ichiki , Masatoshi Shiino

The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…

Probability · Mathematics 2016-09-07 P. Vellaisamy , A. Kumar

The escape from a given domain is one of the fundamental problems in statistical physics and the theory of stochastic processes. Here, we explore properties of the escape of an inertial particle driven by L\'evy noise from a bounded domain,…

Statistical Mechanics · Physics 2021-08-25 Karol Capała , Bartłomiej Dybiec

Stochastic evolution of various dynamic systems and reaction networks is commonly described in terms of noise assisted escape of an overdamped particle from a potential well, as devised by the paradigmatic Langevin equation in which…

Statistical Mechanics · Physics 2020-03-16 Karol Capała , Bartłomiej Dybiec , Ewa Gudowska-Nowak

We establish the large deviation principle for the slow variables in slow-fast dynamical system driven by both Brownian noises and L\'evy noises. The fast variables evolve at much faster time scale than the slow variables, but they are…

Dynamical Systems · Mathematics 2022-11-22 Shenglan Yuan , René Schilling , Jinqiao Duan

We consider the motion of an overdamped particle in a force field in presence of an external, adiabatic noise, without the restriction that the noise process is Gaussian or the stochastic process is Markovian. We examine the condition for…

Statistical Mechanics · Physics 2007-05-23 Suman Kumar Banik , Jyotipratim Ray Chaudhuri , Deb Shankar Ray

With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…

Machine Learning · Statistics 2021-02-03 Yang Li , Jinqiao Duan

Many-body and complex systems, both classical and quantum, often exhibit slow, nonlinear relaxation toward stationary states due to the presence of metastable configurations and environmental fluctuations. Nonlinear relaxation in a wide…

Statistical Mechanics · Physics 2026-02-02 Claudio Guarcello , Alexander A. Dubkov , Davide Valenti , Bernardo Spagnolo

The mean first exit (passage) time characterizes the average time of a stochastic process never leaving a fixed region in the state space, while the escape probability describes the likelihood of a transition from one region to another for…

Probability · Mathematics 2017-02-28 Weihua Deng , Xiaochao Wu , Wanli Wang