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Stochastic partial differential equations and stochastic controls

open access: yesStochastic partial differential equations and stochastic controls
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Stochastic partial differential equations

2014
Second 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 AND TURBULENCE

Mathematical Models and Methods in Applied Sciences, 1991
Stochastic partial differential equations are proposed in order to model some turbulence phenomena. A particular case (the stochastic Burgers equations) is studied. Global existence of solutions is proved. Their regularity is also studied in detail. It is shown that the solutions cannot possess too high regularity.
Brzeźniak, Z.   +2 more
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Adaptive Concepts for Stochastic Partial Differential Equations

Journal of Scientific Computing, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreas Prohl, Christian Schellnegger
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ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Mathematics of the USSR-Sbornik, 1975
In 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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On the approximation of stochastic partial differential equations i

Stochastics, 1988
The stability of abstract stochastic partial differential equations with respect to the simultaneous perturbation of the driving processes and of the differential operators is investigated. The results obtained here will be applied to concrete stochastic partial differential equations in the continuation of this ...
I Gyöngy
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Invariant manifolds for stochastic partial differential equations

open access: yesAnnals of Probability, 2003
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
Kening Lu   +2 more
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