English
Related papers

Related papers: First-Exit Time Analysis for Truncated Heavy-Taile…

200 papers

For many stochastic dynamic systems, the Mean First Passage Time (MFPT) is a useful concept, which gives expected time before a state of interest. This work is an extension of MFPT in several ways. (1) We show that for some systems the…

Systems and Control · Computer Science 2014-12-23 Cenk Oguz Saglam , Katie Byl

Heavy-tailed stochastic gradient noise, commonly observed in transformer models, can destabilize the optimization process. Recent works mainly focus on developing and understanding approaches to address heavy-tailed noise in the centralized…

Machine Learning · Computer Science 2026-02-23 Junfei Sun , Dixi Yao , Xuchen Gong , Tahseen Rabbani , Manzil Zaheer , Tian Li

This paper focuses on the strong convergence of the truncated $\theta$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate,…

Numerical Analysis · Mathematics 2021-12-28 Shuaibin Gao , Junhao Hu , Jie He , Qian Guo

In this paper, we aim to study the asymptotic behavior for multi-scale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviation between the slow component $X^{\varepsilon}$ and the…

Probability · Mathematics 2023-06-02 Wei Hong , Shihu Li , Wei Liu , Xiaobin Sun

A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form $\dot x_1=u$, $\dot x_j=x_1^{j-1}$, $j=2,\ldots,n$, is obtained for arbitrary $n$. The main goal of the paper is to present the…

Optimization and Control · Mathematics 2020-07-07 Grigory M. Sklyar , Svetlana Yu. Ignatovich

We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…

Optimization and Control · Mathematics 2026-04-02 Antoine Marie Bogso , Rhoss Likibi Pellat , Wilfried Kuissi Kamdem , Olivier Menoukeu Pamen

We analyse large deviations of time-averaged quantities in stochastic processes with long-range memory, where the dynamics at time t depends itself on the value q_t of the time-averaged quantity. First we consider the elephant random walk…

Statistical Mechanics · Physics 2020-08-05 Robert L. Jack , Rosemary J. Harris

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…

Statistical Mechanics · Physics 2015-06-24 Guy Fayolle , Cyril Furtlehner

Motivated by the recent interest in risk-aware control, we study a continuous-time control synthesis problem to bound the risk that a stochastic linear system violates a given specification. We use risk signal temporal logic as a…

Systems and Control · Electrical Eng. & Systems 2022-04-12 Sleiman Safaoui , Lars Lindemann , Iman Shames , Tyler H. Summers

We examine a class of stochastic differential inclusions involving multiscale effects designed to solve a class of generalized variational inequalities. This class of problems contains constrained convex non-smooth optimization problems,…

Optimization and Control · Mathematics 2026-01-23 D. Russell Luke , Johannes-Carl Schnebel , Mathias Staudigl , Juan Peypouquet , Siqi Qu

This article concerns the large deviations regime and the consequent solution of the Kramers problem for a two-time scale stochastic system driven by a common jump noise signal perturbed in small intensity $\varepsilon>0$ and with…

Probability · Mathematics 2022-07-15 Pedro Catuogno , André de Oliveira Gomes

Current is a characteristic feature of nonequilibrium systems. In stochastic systems, these currents exhibit fluctuations constrained by the rate of dissipation in accordance with the recently discovered thermodynamic uncertainty relation.…

Statistical Mechanics · Physics 2017-10-30 Todd R. Gingrich , Jordan M. Horowitz

This paper mainly investigates the strong convergence and stability of the truncated Euler-Maruyama (EM) method for stochastic differential delay equations with variable delay whose coefficients can be growing super-linearly. By…

Numerical Analysis · Mathematics 2021-08-10 Shounian Deng , Chen Fei , Weiyin Fei , Xuerong Mao

We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft…

Probability · Mathematics 2010-01-20 Arijit Chakrabarty , Gennady Samorodnitsky

We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for…

Statistical Mechanics · Physics 2025-05-14 Izaak Neri

The first passage times for enzymatic turnovers in non-equilibrium steady state display a statistical symmetry property related to non-equilibrium fluctuation theorems, that makes it possible to extract the chemical driving force from…

Biological Physics · Physics 2008-12-10 Martin Lindén

We consider a one-dimensional fluctuating interfacial profile governed by the Edwards-Wilkinson or the stochastic Mullins-Herring equation for periodic, standard Dirichlet and Dirichlet no-flux boundary conditions. The minimum action path…

Statistical Mechanics · Physics 2018-03-28 Markus Gross

Temporal difference (TD) methods constitute a class of methods for learning predictions in multi-step prediction problems, parameterized by a recency factor lambda. Currently the most important application of these methods is to temporal…

Artificial Intelligence · Computer Science 2008-02-03 P. Cichosz

Considering the use of dynamical systems in practical applications, often only limited regions in the time or frequency domain are of interest. Therefor, it usually pays off to compute local approximations of the used dynamical systems in…

Optimization and Control · Mathematics 2021-05-17 Peter Benner , Steffen W. R. Werner

This paper establishes a stochastic maximum principle for optimal control problems governed by time-changed forward-backward stochastic differential equations with L\'evy noise. The system incorporates a random, non-decreasing operational…

Optimization and Control · Mathematics 2026-03-27 Jingwei Chen , Jun Ye , Feng Chen