The Harmonic Functions of Mean Ergodic Markov Semigroups.
The Harmonie Space Associated with a "Reasonable" Standard Process.
The Hausdorff a-Dimensional Measures of the Level Sets and the Graph of the TV-Parameter Wiener Process.
The heat equation on manifolds as a gradient flow in the Wasserstein space
We study the gradient flow for the relative entropy functional on probability measures over a riemannian manifold. To this aim we present a notion of a riemannian structure on the Wasserstein space. If the Ricci curvature is bounded below we establish existence and contractivity of the gradient flow using a discrete approximation scheme. Furthermore we show that its trajectories coincide with solutions to the heat equation.
The hypercontractivity of Ornstein-Uhlenbeck semigroups with drift, revisited
The infinite Brownian loop on a symmetric space.
The infinite valley for a recurrent random walk in random environment
We consider a one-dimensional recurrent random walk in random environment (RWRE). We show that the – suitably centered – empirical distributions of the RWRE converge weakly to a certain limit law which describes the stationary distribution of a random walk in an infinite valley. The construction of the infinite valley goes back to Golosov, see Comm. Math. Phys.92 (1984) 491–506. As a consequence, we show weak convergence for both the maximal local time and the self-intersection local time of the...
The island model as a Markov dynamic system
Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators....
The Kendall theorem and its application to the geometric ergodicity of Markov chains
We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of...
The Kiefer-Wolfowitz approximation method in controlled Markov chains
The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types.
The Kolmogorov equation with time-measurable coefficients.
The largest component in an inhomogeneous random intersection graph with clustering.
The law of the hitting times to points by a stable Lev́y process with no negative jumps.
The law of the maximum of a Bessel bridge.
The laws of Chung and Hirsch for Cauchy's principal values related to Brownian local times.
The Lenz shift and wiener sausage in riemannian manifolds
The level sets of iterated brownian motion
The lifetime of conditional brownian motion in the plane
The lifetimes of conditioned diffusion processes