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Related papers: Euler-Maruyama method for non-Wiener processes

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The aim of this study is to find a generic method for generating a path of the solution of a given stochastic differential equation which is more efficient than the standard Euler-Maruyama scheme with Gaussian increments. First we…

Probability · Mathematics 2019-09-11 Masaaki Fukasawa , Jan Obloj

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…

Probability · Mathematics 2020-11-25 Martin Hutzenthaler , Arnulf Jentzen

Nowadays many tools, e.g. fluctuation relations, are available to characterize the statistical properties of non-equilibrium systems. However, most of these tools rely on the assumption that the driving noise is normally distributed. Here…

Statistical Mechanics · Physics 2023-11-29 Dario Lucente , Andrea Puglisi , Massimiliano Viale , Angelo Vulpiani

We analyze the statistical performance of identification of stochastic dynamical systems with non-linear measurement sensors. This includes stochastic Wiener systems, with linear dynamics, process noise and measured by a non-linear sensor…

Optimization and Control · Mathematics 2018-05-24 Bo Wahlberg , Lennart Ljung

We present a method, based on the Keldysh formalism, for deriving stochastic master equations that describe the non-Markovian dynamics of a quantum system coupled to a Gaussian environment. This approach yields a compact expression for the…

Quantum Physics · Physics 2026-01-21 Vasco Cavina , Antonio D'Abbruzzo , Vittorio Giovannetti

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

In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…

Probability · Mathematics 2019-01-16 Nicolas Marie

We analyze energetics of a non-Gaussian process described by a stochastic differential equation of the Langevin type. The process represents a paradigmatic model of a nonequilibrium system subject to thermal fluctuations and additional…

Statistical Mechanics · Physics 2015-06-16 L. Kusmierz , J. M. Rubi , E. Gudowska-Nowak

By introducing a new stochastic integral, we investigate the energetics of classical stochastic systems driven by non-Gaussian white noises. In particular, we introduce a decomposition of the total-energy difference into the work and the…

Statistical Mechanics · Physics 2012-05-23 Kiyoshi Kanazawa , Takahiro Sagawa , Hisao Hayakawa

A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the…

Statistical Mechanics · Physics 2009-05-06 Bartlomiej Dybiec , Ewa Gudowska-Nowak

Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation…

Statistics Theory · Mathematics 2014-01-23 Jugalkishore K. Banoth , Pradip Sircar

3D stochastic Euler equations with a special form of multiplicative noise are considered. A Constantin-Iyer type representation in Euler-Lagrangian form is given, based on stochastic characteristics. Local existence and uniqueness of…

Probability · Mathematics 2018-03-15 Franco Flandoli , Dejun Luo

We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…

Computation · Statistics 2016-04-26 Gavin A. Whitaker , Andrew Golightly , Richard J. Boys , Chris Sherlock

A dynamical system driven by non-Gaussian L\'evy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian L\'evy…

Dynamical Systems · Mathematics 2008-08-08 Zhihui Yang , Jinqiao Duan

Using the Euler-Maruyama numerical method, we present calculations of the Ermakov-Lewis invariant and the dynamic, geometric, and total phases for several cases of stochastic parametric oscillators, including the simplest case of the…

Chaotic Dynamics · Physics 2014-10-22 E. Cervantes-Lopez , P. B. Espinoza , A. Gallegos , H. C. Rosu

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

Numerical Analysis · Mathematics 2015-03-13 Jiarui Yang , Jinqiao Duan

Non-equilibrium noise is characterized as noise realizations where external agitations disrupt the harmonic equilibrium of Brownian motion. Excitations in a particle's random walk into a so-called L\'evy flight changes the distribution of…

Statistical Mechanics · Physics 2024-06-25 Noah M. MacKay

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, L\'evy and stretched Gaussian noises, to exact value of the selected…

Other Statistics · Statistics 2018-01-17 Wei Xu , Wen Chen , Yingjie Liang

We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…

Machine Learning · Statistics 2017-03-31 Maziar Raissi , Paris Perdikaris , George Em Karniadakis

Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and play an important role in quantifying propagation and evolution of uncertainty. Although Fokker-Planck equations can be written…

Dynamical Systems · Mathematics 2016-03-17 Xu Sun , Jinqiao Duan , Xiaofan Li , Hua Liu , Xiangjun Wang , Yayun Zheng