2 Solutions of equation with a reflection measure 10 2.1 Pathwise uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Convergence of invariants measures . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Existence of stationary solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Convergence of the semigroup . . . . . . . . . . ....

We prove that a Moran model converges in probability to Eigen's quasispecies model in the infinite population limit. We show further that the invariant probability measure of the Moran model converges to the unique stationary solution of Eigen's quasispecies model.

We consider a stochastic variant of the game of Bulgarian solitaire [9]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type.

We are going to give necessary and suucient conditions for a multivariate stationary stochastic process to be completely regular. We also give the answer to a question of V.V. Peller concerning the spectral measure characterization of such processes .

We consider a stochastic variant of the game of Bulgarian solitaire [9]. For the stationary measure of the random Bulgarian solitaire, we prove that most of its mass is concentrated on (roughly) triangular configurations of certain type.

We prove that the stationary measure associated to a boundary driven exclusion process in any dimension satisfies a large deviation principle with rate function given by the quasi potential of the Freidlin and Wentzell theory.

We study critical and stationary, i.e., with respect to both inner outer variations, points of polyconvex functionals the form for . In particular, we show that a.e. have locally constant determinant except in a relatively closed set measure zero, stationary almost everywhere. This is deduced from more general result concerning solutions , linearized problem also present some generalization ori...

We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Lévy measure as characteristic of a Maharam system. This allows us to derive structural results and their ergodic consequences. 1. Introduction. In a fundamental paper [9], Rosi´nski revealed the hidden structure of stationary symmetric α-stable (SαS) processes. Namely, he proved t...

Consider a stochastic process {x(t), t€T} of random elements of a Hilbert space H, whose index set is a locally compact Hausdorff space. The results obtained in this work fall into two broad categories, first the study of weakly stationary processes and their representations, and secondly the study of the sample path properties of not necessarily . stationary processes. In each case, we choose ...

We consider invariant measures for the stochastic Burgers equation on \({\mathbb {R}}\), forced by derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth space. An measure indecomposable, or extremal, if it cannot be represented as convex combination other measures. show each \(a\in {\mathbb there unique indecomposable law spacetime-stationary solution with mean a...