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We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be…

Statistical Mechanics · Physics 2009-11-11 Giovanni Bonanno , Davide Valenti , Bernardo Spagnolo

With the rapid increase of valuable observational, experimental and simulated data for complex systems, much efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the wide applications of…

Machine Learning · Statistics 2021-10-01 Yang Li , Yubin Lu , Shengyuan Xu , Jinqiao Duan

In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bi-variate $\alpha$-stable L\'evy type noise from a 2-dimensional disk. For an appropriate choice of parameters the mean first passage…

Statistical Mechanics · Physics 2020-03-16 Krzysztof Szczepaniec , Bartlomiej Dybiec

In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents.…

Probability · Mathematics 2019-11-13 Tomasz Grzywny

We present a method to learn mean residence time and escape probability from data modeled by stochastic differential equations. This method is a combination of machine learning from data (to extract stochastic differential equations as…

Dynamical Systems · Mathematics 2019-10-02 Dengfeng Wu , Miaomiao Fu , 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

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

Properties of the noise-driven escape kinetics are mainly determined by the stochastic component of the system dynamics. Nevertheless, the escape dynamics is also sensitive to deterministic forces. Here, we are exploring properties of the…

Statistical Mechanics · Physics 2022-06-30 Karol Capała , Bartłomiej Dybiec

We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by {\it white L\'evy noise} in a dynamical regime where inertial effects can safely be neglected. The…

Statistical Mechanics · Physics 2009-11-11 B. Dybiec E. Gudowska-Nowak P. Hänggi

In this paper we study first exit times from a bounded domain of a gradient dynamical system $\dot Y_t=-\nabla U(Y_t)$ perturbed by a small multiplicative L\'evy noise with heavy tails. A special attention is paid to the way the…

Probability · Mathematics 2015-03-20 Ilya Pavlyukevich

We consider a finite dimensional deterministic dynamical system with a global attractor A with a unique ergodic measure P concentrated on it, which is uniformly parametrized by the mean of the trajectories in a bounded set D containing A.…

Probability · Mathematics 2013-03-21 Michael Högele , Ilya Pavlyukevich

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

Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between…

Dynamical Systems · Mathematics 2025-10-20 Jinqiao Duan , James R. Brannan , Vincent J. Ervin

Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous physical phenomena exhibiting bursting, flights, hopping, and…

Statistics Theory · Mathematics 2022-02-09 Yang Li , Jinqiao Duan

The escape from a potential well is an archetypal problem in the study of stochastic dynamical systems, representing real-world situations from chemical reactions to leaving an established home range in movement ecology. Concurrently,…

Statistical Mechanics · Physics 2021-02-03 Karol Capala , Amin Padash , Aleksei V. Chechkin , Babak Shokri , Ralf Metzler , Bartlomiej Dybiec

The mean exit time escaping basin of attraction in the presence of white noise is of practical importance in various scientific fields. In this work, we propose a strategy to control mean exit time of general stochastic dynamical systems to…

Machine Learning · Statistics 2023-08-09 Yang Li , Shenglan Yuan , Shengyuan Xu

The L\'evy walk process for the lower interval of the time of flight distribution ($\alpha<1$) and with finite resting time between consecutive flights is discussed. The motion is restricted to a region bounded by two absorbing barriers and…

Statistical Mechanics · Physics 2023-07-19 A. Kamińska , T. Srokowski

First-passage properties of continuous stochastic processes confined in a 1--dimensional interval are well described. However, for jump processes (discrete random walks), the characterization of the corresponding observables remains…

Statistical Mechanics · Physics 2023-05-17 Jérémie Klinger , Raphaël Voituriez , Olivier Bénichou

Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…

Probability · Mathematics 2025-08-06 Eric José Ávila-Vales , José Villa-Morales

Non-Gaussian noise influences many complex out-of-equilibrium systems on a wide range of scales such as quantum devices, active and living matter, and financial markets. Despite the ubiquitous nature of non-Gaussian noise, its effect on…

Statistical Mechanics · Physics 2022-09-01 Adrian Baule , Peter Sollich