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Motivated by their broad applications in reinforcement learning, we study the linear two-time-scale stochastic approximation, an iterative method using two different step sizes for finding the solutions of a system of two equations. Our…

Machine Learning · Computer Science 2020-01-13 Thinh T. Doan

Stochastic phenomena in which the noise amplitude is proportional to the fluctuating variable itself, usually called {\it multiplicative noise}, appear ubiquitously in physics, biology, economy and social sciences. The properties of…

Condensed Matter · Physics 2007-05-23 Miguel A. Munoz

A spatially extended Lotka-Volterra system of two competing species in the presence of two correlated noise sources is analyzed: (i) an external multiplicative time correlated noise, which mimics the interaction between the system and the…

Statistical Mechanics · Physics 2007-05-23 D. Valenti , L. Schimansky-Geier , X. Sailer , B. Spagnolo , M. Iacomi

This paper focuses on deriving optimal-order full moment error estimates in strong norms for both velocity and pressure approximations in the Euler-Maruyama time discretization of the stochastic Navier-Stokes equations with multiplicative…

Numerical Analysis · Mathematics 2025-10-10 Xiaobing Feng , Liet Vo

This paper is concerned with the stochastic thermodynamics of non-equilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus,…

Statistical Mechanics · Physics 2022-12-20 S. Mohsen J. Khadem , Rainer Klages , Sabine H. L. Klapp

In this introductory work I will present the Finite Difference method for hyperbolic equations, focusing on a method which has second order precision both in time and space (the so-called staggered leapfrog method) and applying it to the…

Computational Physics · Physics 2007-05-23 Artur B. Adib

In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…

Numerical Analysis · Mathematics 2022-01-27 Daxin Nie , Jing Sun , Weihua Deng

We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven by Brownian motion, it has been shown that in order for the…

Statistics Theory · Mathematics 2025-05-14 Pablo Ramses Alonso-Martin , Horatio Boedihardjo , Anastasia Papavasiliou

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance. In the classical setting when noise has finite variance, an optimal algorithm, built upon the…

The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external…

Statistical Mechanics · Physics 2023-08-31 Yingjie Liang , Wei Wang , Ralf Metzler

In this article we study effects that small perturbations in the noise have to the solution of differential equations driven by H\"older continuous functions of order $H>\frac12$. As an application, we consider stochastic differential…

Probability · Mathematics 2020-05-11 Lauri Viitasaari , Caibin Zeng

High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…

Machine Learning · Statistics 2021-07-21 Liang Ding , Rui Tuo , Xiaowei Zhang

This study addresses limited attention allocation in a stochastic linear quadratic system with multiplicative noise. Our approach enables strategic resource allocation to enhance noise estimation and improve control decisions. We provide…

Optimization and Control · Mathematics 2024-03-28 Xiangyu Cui , Jianjun Gao , Lingjie Kong

This paper studies the spectrum assignment of a class of stochastic systems with multiplicative noise. A novel $\alpha$-spectrum assignment is proposed for discrete-time and continuous-time stochastic systems with multiplicative noise. In…

Optimization and Control · Mathematics 2025-04-04 Xiaomin Xue , Juanjuan Xu , Huanshui Zhang

In this paper we prove, for small Hurst parameters, the higher order differentiability of a stochastic flow associated with a stochastic differential equation driven by an additive multi-dimensional fractional Brownian noise, where the…

Probability · Mathematics 2018-05-15 Oussama Amine , David R. Baños , Frank Proske

We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…

Artificial Intelligence · Computer Science 2023-01-02 Dimitri Bertsekas

In this paper, we consider both first- and second-order techniques to address continuous optimization problems arising in machine learning. In the first-order case, we propose a framework of transition from deterministic or…

Machine Learning · Computer Science 2021-11-30 Sanae Lotfi , Tiphaine Bonniot de Ruisselet , Dominique Orban , Andrea Lodi

In this work, we investigate the multimode Brownian oscillators in nonequilibrium scenarios with multiple reservoirs at different temperatures. For this purpose, an algebraic method is proposed. This approach gives the exact time-local…

Statistical Mechanics · Physics 2023-07-12 Xin-Hai Tong , Hong Gong , Yao Wang , Rui-Xue Xu , YiJing Yan

Leapfrog integration has been the method of choice in N-body simulations owing to its low computational cost for a symplectic integrator with second order accuracy. We introduce a new leapfrog integrator that allows for variable timesteps…

Astrophysics · Physics 2007-05-23 Thomas Quinn , Neal Katz , Joachim Stadel , George Lake

The Brownian motion of microscopic particles is driven by the collisions with the molecules of the surrounding fluid. The noise associated with these collisions is not white, but coloured due, e.g., to the presence of hydrodynamic memory.…

Statistical Mechanics · Physics 2012-10-04 Scott Hottovy , Giovanni Volpe , Jan Wehr