Quasilinear parabolic stochastic partial differential equations: existence, uniqueness [PDF]
, 2015 In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone nor locally ...
Hofmanova, Martina, Zhang, Tusheng
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Density estimates on a parabolic spde [PDF]
, 2002 We consider a general class of parabolic spde's [formula] with (t, x) [member of] [0, T]×[0, 1] and [epsilon]Wt,x, [epsilon] > 0, a perturbed Gaussian space-time white noise. For (t, x) [member of] (0, T]×(0, 1) we prove the called Davies and Varadhan-
Mellouk, M., Márquez-Carreras, D.
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A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise [PDF]
, 2007 A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation.
Lototsky, S. V.
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Optimizing the Fractional Power in a Model with Stochastic PDE Constraints
Advanced Nonlinear Studies, 2018 We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter s is the s-th power of the diffusion operator in the state equation.
Geldhauser Carina, Valdinoci Enrico
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A note on maximal estimates for stochastic convolutions [PDF]
, 2010 In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces ...
A. Friedman +32 more
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Invariant measures for monotone SPDE's with multiplicative noise term
, 2012 We study diffusion processes corresponding to infinite dimensional semilinear stochastic differential equations with local Lipschitz drift term and an arbitrary Lipschitz diffusion coefficient.
Es-Sarhir, A. +3 more
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Solution theory of fractional SDEs in complete subcritical regimes
Forum of Mathematics, SigmaWe consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense.
Lucio Galeati, Máté Gerencsér
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Estimates for the ergodic measure and polynomial stability of plane stochastic curve shortening flow
, 2010 We establish moment estimates for the invariant measure of a stochastic partial differential equation describing motion by mean curvature flow in (1+1) dimension, leading to polynomial stability of the associated Markov semigroup.
A. Es-Sarhir +8 more
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Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs [PDF]
, 2010 Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme.
Kloeden, Peter E., Shott, Stephen
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Well-posedness of the stochastic transport equation with unbounded drift
, 2017 The Cauchy problem for a multidimensional linear transport equation with unbounded drift is investigated. Provided the drift is Holder continuous , existence, uniqueness and strong stability of solutions are obtained.
Mollinedo, David A. C. +1 more
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