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Stochastic calculus of variations for stochastic partial differential equations
Journal of Functional Analysis, 1988 AbstractThis paper develops the stochastic calculus of variations for Hilbert space-valued solutions to stochastic evolution equations whose operators satisfy a coercivity condition. An application is made to the solutions of a class of stochastic pde's which includes the Zakai equation of nonlinear filtering.
Daniel Ocone
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Invariant manifolds for stochastic partial differential equations
The Annals of Probability, 2004 Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant
Jinqiao Duan +2 more
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Postprocessing for Stochastic Parabolic Partial Differential Equations [PDF]
SIAM Journal on Numerical Analysis, 2007 We investigate the strong approximation of stochastic parabolic partial differential equations with additive noise. We introduce postprocessing in the context of a standard Galerkin approximation, although other spatial discretizations are possible. In time, we follow [G. J. Lord and J. Rougemont, IMA J. Numer. Anal., 24 (2004), pp. 587-604] and use an
Gabriel J. Lord, Tony Shardlow
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Regularities for semilinear stochastic partial differential equations
Journal of Functional Analysis, 2007 AbstractIn this paper, we study the regularities of solutions to semilinear stochastic partial differential equations in general settings, and prove that the solution can be smooth arbitrarily when the data is sufficiently regular. As applications, we also study several classes of semilinear stochastic partial differential equations on abstract Wiener ...
Xicheng Zhang
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Amplitude Equations for Stochastic Partial Differential Equations [PDF]
, 2007 Dirk Blömker
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Large deviations for stochastic Kuramoto–Sivashinsky equation with multiplicative noise
Nonlinear Analysis, 2021 The Kuramoto–Sivashinsky equation is a nonlinear parabolic partial differential equation, which describes the instability and turbulence of waves in chemical reactions and laminar flames. The aim of this work is to prove the large deviation principle for
Gregory Amali Paul Rose +2 more
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On Some Results of the Nonuniqueness of Solutions Obtained by the Feynman–Kac Formula
Mathematics, 2023 The Feynman–Kac formula establishes a link between parabolic partial differential equations and stochastic processes in the context of the Schrödinger equation in quantum mechanics.
Byoung Seon Choi, Moo Young Choi
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Complexity, 2023 In this article, we consider the Nash equilibrium of stochastic differential game where the state process is governed by a controlled stochastic partial differential equation and the information available to the controllers is possibly less than the ...
Gaofeng Zong
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The Osgood condition for stochastic partial differential equations [PDF]
Bernoulli, 2021 We study the following equation \begin{equation*} \frac{\partial u(t,\,x)}{\partial t}= u(t,\,x)+b(u(t,\,x))+ \dot{W}(t,\,x),\quad t>0, \end{equation*} where $ $ is a positive constant and $\dot{W}$ is a space-time white noise. The initial condition $u(0,x)=u_0(x)$ is assumed to be a nonnegative and continuous function.
Foondun, Mohammud, Nualart, Eulalia
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Using Nonlinear Diffusion Model to Identify Music Signals
Advances in Mathematical Physics, 2021 In this paper, combined with the partial differential equation music signal smoothing model, a new music signal recognition model is proposed. Experimental results show that this model has the advantages of the above two models at the same time, which ...
Qiang Li
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