Random attractors for locally monotone stochastic partial differential equations
Journal of Differential Equations, 2019 We prove the existence of random dynamical systems and random attractors for a large class of locally monotone stochastic partial differential equations perturbed by additive L\'{e}vy noise.
B. Gess, W. Liu, Andre Schenke
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Controllability of semilinear stochastic delay evolution equations in Hilbert spaces
International Journal of Mathematics and Mathematical Sciences, 2002 The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given.
P. Balasubramaniam, J. P. Dauer
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Pseudo-Likelihood Estimation for Parameters of Stochastic Time-Fractional Diffusion Equations
Fractal and Fractional, 2021 Although stochastic fractional partial differential equations have received increasing attention in the last decade, the parameter estimation of these equations has been seldom reported in literature.
Guofei Pang, Wanrong Cao
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Some recent progress in singular stochastic partial differential equations
Bulletin of the American Mathematical Society, 2019 . Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment.
Ivan Corwin, Hao Shen
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Averaged Systems of Stochastic Differential Equations with Lévy Noise and Fractional Brownian Motion
Fractal and FractionalIn some problems, partial differential equations are reduced to ordinary differential equations. In special cases, when incorporating randomness, equations can be reduced to systems of stochastic differential Equations (SDEs).
Tayeb Blouhi +6 more
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Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives [PDF]
SIAM Journal on Mathematical Analysis, 2017 In this paper we develop a method to solve (stochastic) evolution equations on Gelfand triples with time-fractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasi-linear partial differential equations
W. Liu, M. Röckner, J. L. D. Silva
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A Proposed Stochastic Finite Difference Approach Based on Homogenous Chaos Expansion
Journal of Applied Mathematics, 2013 This paper proposes a stochastic finite difference approach, based on homogenous chaos expansion (SFDHC). The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In
O. H. Galal
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Two-time-scale stochastic partial differential equations driven by $\alpha $-stable noises: Averaging principles [PDF]
, 2016 This paper focuses on stochastic partial differential equations (SPDEs) under two-time-scale formulation. Distinct from the work in the existing literature, the systems are driven by $\alpha$-stable processes with $\alpha \in(1,2)$.
J. Bao, G. Yin, C. Yuan
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Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks [PDF]
Journal of Computational Physics, 2019 Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions, etc. Because of
Sharmila Karumuri +3 more
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Approximations of stochastic partial differential equations
The Annals of Applied Probability, 2016 In this paper we show that solutions of stochastic partial differential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.
Di Nunno, Giulia, Zhang, Tusheng
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