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Stochastic partial differential equations and stochastic controls
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Stochastic partial differential equations
Computer Vision, 2014Second order stochastic partial differential equations are discussed from a rough path point of view. In the linear and finite-dimensional noise case we follow a Feynman–Kac approach which makes good use of concentration of measure results, as those obtained in Sect. 11.2.
Peter K. Friz, Martin Hairer
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Stochastic Partial Differential Equations
É. Pardoux
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Stochastics and Dynamics, 2008
In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic ...
Boufoussi, B., Mrhardy, N.
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In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic ...
Boufoussi, B., Mrhardy, N.
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Asymptotic behavior of multiscale stochastic partial differential equations with Hölder coefficients
Journal of Functional Analysis, 2020In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the averaging ...
M. Rockner, Longjie Xie, Li Yang
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Neutral fractional stochastic partial differential equations with Clarke subdifferential
Applicable Analysis, 2020By using fractional calculus, stochastic analysis theory and fixed point theorems, sufficient conditions for approximate controllability of nonlocal Sobolev-type neutral fractional stochastic differential equations with fractional Brownian motion and ...
H. Ahmed, H. El-Owaidy, M. A. Al-Nahhas
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Stochastic Partial Differential Equations
2017Sergey V. Lototsky, Boris L. Rozovsky
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ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
Mathematics of the USSR-Sbornik, 1975In this paper we consider the Cauchy problem for second-order stochastic partial differential equations of parabolic type. We study linear and nonlinear equations for filtering Markov diffusion processes. Theorems on the existence, uniqueness and smoothness of solutions are proved.Bibliography: 21 items.
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Travelling Waves in Monostable and Bistable Stochastic Partial Differential Equations
Jahresbericht Der Deutschen Mathematiker-vereinigung, 2019In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stochastic partial differential equations (SPDEs).
C. Kuehn
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