Results 31 to 40 of about 2,307 (91)
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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Galerkin approximation and the strong solution of the Navier‐Stokes equation
International Journal of Stochastic Analysis, Volume 13, Issue 3, Page 239-259, 2000., 2000 We consider a stochastic equation of Navier‐Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Hannelore Breckner
wiley +1 more source
PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES
Forum of Mathematics, Pi, 2015 We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths.
MASSIMILIANO GUBINELLI +2 more
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Periodic in distribution solution for a telegraph equation
International Journal of Stochastic Analysis, Volume 12, Issue 2, Page 121-131, 1999., 1998 In this paper we study an abstract stochastic equation of second order and stochastic boundary problem for the telegraph equation in a strip. We prove the existence of solutions, which are d‐periodic (periodic in distribution) random processes.
A. Ya. Dorogovtsev
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A non‐nonstandard proof of Reimers′ existence result for heat SPDEs
International Journal of Stochastic Analysis, Volume 11, Issue 1, Page 29-41, 1998., 1997 In 1989, Reimers gave a nonstandard proof of the existence of a solution to heat SPDEs, driven by space‐time white noise, when the diffusion coefficient is continuous and satisfies a linear growth condition. Using the martingale problem approach, we give a non‐nonstandard proof of this fact, and with the aid of Girsanov′s theorem for continuous ...
Hassan Allouba
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A CLASS OF GROWTH MODELS RESCALING TO KPZ
Forum of Mathematics, Pi, 2018 We consider a large class of $1+1$-dimensional continuous interface growth models and we show that, in both the weakly asymmetric and the intermediate disorder regimes, these models converge to Hopf–Cole solutions to the KPZ equation.
MARTIN HAIRER, JEREMY QUASTEL
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A comparison theorem for backward SPDEs with jumps
, 2014 In this paper we obtain a comparison theorem for backward stochastic partial differential equation (SPDEs) with jumps. We apply it to introduce space-dependent convex risk measures as a model for risk in large systems of interacting ...
Sulem, Agnès +2 more
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Stability of stationary and periodic solutions equations in Banach space
International Journal of Stochastic Analysis, Volume 10, Issue 3, Page 249-255, 1997., 1997 Linear difference and differential equations with operator coefficients and random stationary (periodic) input are considered. Conditions are presented for the mean stability of stationary (periodic) solutions under small perturbation of the coefficients.
A. Ya. Dorogovtsev
wiley +1 more source
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
core
On the (strict) positivity of solutions of the stochastic heat equation
, 2014 We give a new proof of the fact that the solutions of the stochastic heat equation, started with non-negative initial conditions, are strictly positive at positive times. The proof uses concentration of measure arguments for discrete directed polymers in
Flores, Gregorio R. Moreno
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