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BOUNDS FOR KAC’S MASTER EQUATION
Markov chain the n ball random rotation selected at random
2015/7/14
Mark Kac considered a Markov Chain on the n–sphere based on random rotations
in randomly chosen coordinate planes. This same walk was used by Hastings on
the orthogonal group. We show that the walk ...
On the (strict) positivity of solutions of the stochastic heat equation
the stochastic heat equation Probability
2012/6/30
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 ...
Homogenization of a stochastic nonlinear reaction-diffusion equation with a large reaction term: the almost periodic framework
Stochastic Homogenization Almost Periodic Stochastic Reaction-Diffusion Equations Wiener Process
2011/9/21
Abstract: Homogenization of a stochastic nonlinear reaction-diffusion equation with a large non- linear term is considered. Under a general Besicovitch almost periodicity assumption on the coefficient...
A linear stochastic differential equation driven by a fractional Brownian motion with Hurst parameter >1/2
Linear stochastic differential equation Fractional Brownian motion Stochastic calculus Ito formula
2011/9/15
Abstract: Given a fractional Brownian motion \,\,$(B_{t}^{H})_{t\geq 0}$,\, with Hurst parameter \,$> 1/2$\,\,we study the properties of all solutions of \,\,: {equation} X_{t}=B_{t}^{H}+\int_0^t X_{u...
A probabilistic view on the general relativistic Boltzmann equation
General relativity, Boltzmann equation, probability, Markov process
2011/8/24
Abstract: A new probalistic approach to general relativistic kinetic theory is proposed. The general relativistic Boltzmann equation is linked to a new Markov process in a completely intrinsic way. Th...
From a kinetic equation to a diffusion under an anomalous scaling
Anomalous thermal conductivity kinetic limit invariance principle
2011/8/23
Abstract: A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump pro...
A limit equation associated to the solvability of the vacuum Einstein constraint equations using the conformal method
solvability vacuum Einstein constraint equations conformal method
2011/3/2
Let (M, g) be a compact Riemannian manifold on which a tracefree and divergence-free 2 W1,p and a positive function 2 W1,p, p > n,are fixed. In this paper, we study the vacuum Einstein constraint ...
Behaviour near extinction for the Fast Diffusion Equation on bounded domains
Nonlinear evolution singular parabolic fast di usion Harnack asymptotics
2011/1/18
We consider the Fast Di usion Equation ut = um posed in a bounded smooth domain
Rd with homogeneous Dirichlet conditions; the exponent range is ms = (d 2)+=(d + 2) < m < 1.It is known...
Low noise limit for the invariant measure of a multi-dimensional stochastic Allen-Cahn equation
Stochastic reaction-di usion equation Invariant measure Large deviations
2011/1/21
We study the invariant measure of a discretized stochastic Allen-Cahn equation in d+1 dimensions in the low noise limit. We consider a cuboidal domain and impose the two stable
phases as boundary con...
Construction of an isotropic cellular automaton for a reaction-diffusion equation by means of a random walk
reaction-diffusion equation random walk
2010/4/1
We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the re...
The role of the central limit theorem in discovering sharp rates of convergence to equilibrium for the solution of the Kac equation
Berry–Esseen inequalities central limit theorem
2010/12/8
In Dolera, Gabetta and Regazzini [Ann. Appl. Probab. 19 (2009)186–201] it is proved that the total variation distance between the solution f(·, t) of Kac’s equation and the Gaussian density (0,2) has...