Journal ArticleDOI
Moderate deviation principle for a class of stochastic partial differential equations
Parisa Fatheddin,Jie Xiong +1 more
TLDR
The moderate deviation principle is established for a class of stochastic partial differential equations with non-Lipschitz continuous coefficients and derived for two important population models: super-Brownian motion and the Fleming–Viot process.Abstract:
We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two important population models: super-Brownian motion and the Fleming-Viot process.read more
Citations
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A moderate deviation principle for 2-D stochastic Navier–Stokes equations driven by multiplicative Lévy noises ☆
TL;DR: In this article, the authors established a moderate deviation principle for two-dimensional stochastic Navier-Stokes equations driven by multiplicative Levy noises and showed that the weak convergence method introduced by Budhiraja, Dupuis and Ganguly in [3] plays a key role.
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A Moderate Deviation Principle for 2-D Stochastic Navier-Stokes Equations Driven by Multiplicative L\'evy Noises
TL;DR: In this article, a moderate deviation principle for two-dimensional stochastic Navier-Stokes equations driven by multiplicative $L\acute{e}vy$ noises is established.
Journal ArticleDOI
Stochastic 2D primitive equations: Central limit theorem and moderate deviation principle
TL;DR: This is the first result about the limit theorem and the moderate deviations for stochastic primitive equations driven by multiplicative noise and the weak convergence method is established.
Journal ArticleDOI
Moderate deviations for stochastic tidal dynamics equations with multiplicative Gaussian noise
TL;DR: In this article, the authors consider the stochastic tidal dynamics equations perturbed by multiplicative Gaussian noise and discuss some asymptotic behaviors, including a central limit theorem and a moderate deviation.
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Large deviation principle of occupation measures for Non-linear monotone SPDEs
Ran Wang,Jie Xiong,Lihu Xu +2 more
TL;DR: In this paper, a large deviation principle for non-linear monotone stochastic partial differential equations is derived using the hyperexponential recurrence criterion for the occupation measure.
References
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Journal ArticleDOI
Large deviations for infinite dimensional stochastic dynamical systems
TL;DR: In this article, a variational representation for functionals of Brownian motion is used to avoid large deviations analysis of solutions to stochastic differential equations and related processes, where the construction and justification of the approximations can be onerous.
Journal ArticleDOI
An ∞-dimensional inhomogeneous Langevin's equation
TL;DR: In this article, the central limit theorem for interacting diffusions was shown for a modified space of tempered distributions, where W ( t ) is a Brownian motion independent of a Φ′-valued Gaussian random variable γ and L ∗ (s) is an integro-differential operator.
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Large deviations for the Fleming–Viot process with neutral mutation and selection, II
Donald A. Dawson,Shui Feng +1 more
TL;DR: The path-level large deviation results improve the results of Dawson and Feng (1998, Stochastic Process) in three aspects: the state space is more natural, the initial condition is relaxed, and a large deviation principle is established for the Fleming-Viot process with selection.
Journal ArticleDOI
Super-Brownian motion as the unique strong solution to an SPDE
TL;DR: In this paper, a stochastic partial differential equation (SPDE) was derived for super-Brownian motion regarded as a distribution function valued process, and the strong uniqueness for the solution to this SPDE was obtained by an extended Yamada-Watanabe argument.
Journal ArticleDOI
Super-Brownian motion as the unique strong solution to an SPDE
TL;DR: In this article, a stochastic partial differential equation (SPDE) was derived for super-Brownian motion regarded as a distribution function valued process, and the strong uniqueness for the solution to this SPDE was obtained by an extended Yamada-Watanabe argument.