Introduction to stochastic partial differential equations

By Mihály Kovács, Stig Larsson. 2008

1,143 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/57941f658a9a3c16af926daa7943acd8168c945d

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Citations in the corpus

Stochastic evolution equations in UMD Banach spaces (2008, unknown): “, [44]) and u0 :S × Ω → R is an BS ⊗ F0-measurable initial value condition.”
Strong solutions for SPDE with locally monotone coefficients driven by L\'{e}vy noise (2011, background): “The proof can be found in [50], we include it here for the reader’s convenience.”
Global solutions to stochastic reaction–diffusion equations with super-linear drift and multiplicative noise (2019, background): “1) is well posed (see Walsh [28], Chapter 3).”
White noise driven SPDEs with reflection: Existence, uniqueness and large deviation principles (2009, background): “4 in [12], we can show that {gn(x, t), n ≥ 1} is also equicontinuous.”
Intermittence and nonlinear parabolic stochastic partial differential equations (2008, methodology): “9) for all t ≥ 0 and x ∈ R, provided that the stochastic integral exists in the sense of Walsh [36].”
The Kardar-Parisi-Zhang equation and universality class (2011, background): “For more details into the properties of white noise and the cylindrical Weiner process and Itô stochastic integrals with respect to these processes, see [22, 23, 170].”
Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions (2013, methodology): “Walsh, J.B.: An introduction to stochastic partial differential equations.”
Large deviations for infinite dimensional stochastic dynamical systems (2008, background): “= ∫ [0,t]×O f(s,u)B(dsdu), t ∈ [0, T ] is well defined as in Chapter 2 of [28].”
Hitting probabilities and the Hausdorff dimension of the inverse images of anisotropic Gaussian random fields (2009, methodology): “where Gt(x, y) is the Green kernel for the heat equation with Neumann boundary conditions (see Walsh [17]).”
Hitting probabilities for systems of non-linear stochastic heat equations with additive noise (2007, methodology): “5Research supported in part by a grant from the US National Science Foundation.”
Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, unknown): “Walsh in [31].”
Spatial asymptotics for the parabolic Anderson models with generalized time–space Gaussian noise (2016, background): “1) can be solvable in a slightly different sense which is briefly described below; we refer to [12, 18] and [23] for details.”