[書籍][B] Ergodicity for infinite dimensional systems

G Da Prato, J Zabczyk - 1996 - books.google.com
This book is devoted to the asymptotic properties of solutions of stochastic evolution
equations in infinite dimensional spaces. It is divided into three parts: Markovian dynamical …

[書籍][B] Stochastic partial differential equations

H Holden, B Øksendal, J Ubøe, T Zhang, H Holden… - 1996 - Springer
In this chapter we will apply the general theory developed in Chapter 2 to solve various
stochastic partial differential equations (SPDEs). In fact, as pointed out in Chapter 1, our …

Exact solution for the Kardar-Parisi-Zhang equation with flat initial conditions

P Calabrese, P Le Doussal - Physical review letters, 2011 - APS
We provide the first exact calculation of the height distribution at arbitrary time t of the
continuum Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with flat initial …

The stochastic heat equation: Feynman-Kac formula and intermittence

L Bertini, N Cancrini - Journal of statistical Physics, 1995 - Springer
We study, in one space dimension, the heat equation with a random potential that is a white
noise in space and time. This equation is a linearized model for the evolution of a scalar field …

Nonlinear fluctuations of weakly asymmetric interacting particle systems

P Gonçalves, M Jara - Archive for Rational Mechanics and Analysis, 2014 - Springer
We introduce what we call the second-order Boltzmann–Gibbs principle, which allows one
to replace local functionals of a conservative, one-dimensional stochastic process by a …

Fractal burgers equations

P Biler, T Funaki, WA Woyczynski - Journal of differential equations, 1998 - Elsevier
The paper studies local and global in time solutions to a class of multidimensional
generalized Burgers-type equations with a fractional power of the Laplacian in the principal …

Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data

S Mishra, C Schwab - Mathematics of computation, 2012 - ams.org
We consider scalar hyperbolic conservation laws in spatial dimension $ d\geq 1$ with
stochastic initial data. We prove existence and uniqueness of a random-entropy solution and …

[書籍][B] The stable manifold theorem for semilinear stochastic evolution equations and stochastic partial differential equations

SE Mohammed, T Zhang, H Zhao - 2008 - books.google.com
Page 1 MEMOIRS Of the American Mathematical Society Number 9, 17 The Stable Manifold
Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential …

Stratified structure of the Universe and Burgers' equation—a probabilistic approach

S Albeverio, SA Molchanov, D Surgailis - Probability Theory and Related …, 1994 - Springer
The model of the potential turbulence described by the 3-dimensional Burgers' equation with
random initial data was developped by Zeldovich and Shandarin, in order to explain the …

Numerical solution of scalar conservation laws with random flux functions

S Mishra, NH Risebro, C Schwab, S Tokareva - SIAM/ASA Journal on …, 2016 - SIAM
We consider scalar hyperbolic conservation laws in several space dimensions, with a class
of random (and parametric) flux functions. We propose a Karhunen--Loève expansion on the …