Journal ArticleDOI
White noise driven quasilinear SPDEs with reflection
David Nualart,Etienne Pardoux +1 more
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In this article, reflected solutions of the heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise, are studied.Abstract:
We study reflected solutions of the heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise. Roughly speaking, at any point (x, t) where the solutionu(x, t) is strictly positive it obeys the equation, and at a point (x, t) whereu(x, t) is zero we add a force in order to prevent it from becoming negative. This can be viewed as an extension both of one-dimensional SDEs reflected at 0, and of deterministic variational inequalities. An existence and uniqueness result is proved, which relies heavily on new results for a deterministic variational inequality.read more
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Stochastic Equations in Infinite Dimensions
Giuseppe Da Prato,Jerzy Zabczyk +1 more
TL;DR: In this paper, the existence and uniqueness of nonlinear equations with additive and multiplicative noise was investigated. But the authors focused on the uniqueness of solutions and not on the properties of solutions.
Habilitation a diriger des recherches
L’Étude Mathématique,De Quelques Modèles,Issus De La,Physique Statistique,Hors Équilibre,Stéphane Mischler,En Mathématiques,Pierre Degond,Laurent Desvillettes,François Golse,Otared Kavian,Benoît Perthame,Jean-Pierre Puel,Mario Pulvirenti,Mais la vache,savait nager +15 more
TL;DR: Granvorka et al. as discussed by the authors present le Ceregmia de Travail, le document de travail published en 2010 by the International Association of Christians and Jews (IAC) in Haiti.
Book ChapterDOI
Stochastic Interface Models
Amir Dembo,Tadahisa Funaki +1 more
TL;DR: In this article, the scaling limits which pass from the microscopic models to macroscopic level are formulated as classical limit procedures in probability theory such as the law of large numbers, the central limit theorem and the large deviation principles.
Journal ArticleDOI
White noise driven SPDEs with reflection
C. Donati-Martin,Etienne Pardoux +1 more
TL;DR: In this paper, reflected solutions of a nonlinear heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by space-time white noise, are studied.
Journal ArticleDOI
Existence and stability for Fokker–Planck equations with log-concave reference measure
TL;DR: In this article, the authors study Markov processes associated with stochastic differential equations, whose nonlinearities are gradients of convex functionals, and prove a general result of existence of such processes and a priori estimates on the transition probabilities.