Average and deviation for slow-fast stochastic partial differential equations
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TLDR
In this paper, the authors derived an averaged equation for a class of stochastic partial differential equations without any Lipschitz assumption on the slow modes and derived the rate of convergence in probability as a byproduct.About:
This article is published in Journal of Differential Equations.The article was published on 2012-09-01 and is currently open access. It has received 140 citations till now. The article focuses on the topics: Stochastic partial differential equation & Martingale (probability theory).read more
Citations
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Mathematical Modeling in Continuum Mechanics
Roger Temam,Alain Miranville +1 more
TL;DR: In this paper, the authors describe the motion of a system: geometry and kinematics, and describe the fundamental laws of dynamics, including the Cauchy stress-tensor and the Schrodinger equation.
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Strong convergence in averaging principle for stochastic hyperbolic–parabolic equations with two time-scales
TL;DR: In this paper, the existence of an averaging equation eliminating the fast variable for a coupled system is proved under suitable conditions, and an effective dynamics for slow variable which takes the form of stochastic wave equation is derived.
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Averaging principle for one dimensional stochastic Burgers equation
TL;DR: In this article, the authors considered the averaging principle for one dimensional stochastic Burgers equation with slow and fast time-scales and showed that the slow component strongly converges to the solution of the corresponding averaged equation under some suitable conditions.
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Averaging Principle for Systems of Reaction-Diffusion Equations with Polynomial Nonlinearities Perturbed by Multiplicative Noise
TL;DR: It is proved the validity of an averaging principle for a class of systems of slow-fast reaction-diffusion equations with the reaction terms in both equations having polynomial growth, perturbed by a noise of multiplicative type.
References
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Book
Markov Processes: Characterization and Convergence
TL;DR: In this paper, the authors present a flowchart of generator and Markov Processes, and show that the flowchart can be viewed as a branching process of a generator.
Book
Random Perturbations of Dynamical Systems
M. I. Freĭdlin,A. D. Ventt︠s︡elʹ +1 more
TL;DR: In this article, the authors introduce the concept of random perturbations in Dynamical Systems with a Finite Time Interval (FTI) and the Averaging Principle.
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Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
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Compact sets in the spaceL p (O,T; B)
TL;DR: In this paper, a characterization of compact sets in Lp (0, T; B) is given, where 1⩽P⩾∞ and B is a Banach space.
Book
Multidimensional Diffusion Processes
TL;DR: In this paper, the authors propose extension theorems, Martingales, and Compactness, as well as the non-unique case of the Martingale problem, and some estimates on the transition probability functions.