Related papers: Absolute continuity and convergence in variation f…
We derive sufficient conditions for the mixing of all orders of interacting transformations of a spatial Poisson point process, under a zero-type condition in probability and a generalized adaptedness condition. This extends a classical…
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…
The convergence of a sequence of point processes with dependent points, defined by a symmetric function of iid high-dimensional random vectors, to a Poisson random measure is proved. This also implies the convergence of the joint…
We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for…
We discuss a purely variational approach to the total variation flow on metric measure spaces with a doubling measure and a Poincar\'e inequality. We apply the concept of parabolic De Giorgi classes together with upper gradients, Newtonian…
We study properties of temperate non-negative purely atomic measures in the Euclidean space such that the distributional Fourier transform of these measures are pure point ones. A connection between these measures and almost periodicity is…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
We study averaging for Stochastic Differential Equations (SDEs) and Poisson equations. We succeed in obtaining a uniform in time (UiT) averaging result, with a rate, for fully coupled SDE models with super-linearly growing coefficients.…
It is proved that the Poisson measure is a spectral measure of some family of commuting selfadjoint operators acting on a space constructed from some generalization of the moment problem.
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We prove existence and uniqueness of the invariant measure and exponential mixing in the total-variation norm for a class of stochastic differential equations driven by degenerate compound Poisson processes. In addition to mild assumptions…
We consider piecewise deterministic Markov processes with degenerate transition kernels of the "house-of-cards"-type. We use a splitting scheme based on jump times to prove the absolute continuity, as well as some regularity, of the…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…
We consider expanding systems with invariant measures that are uniformly expanding everywhere except on a small measure set and show that the limiting statistics of hitting times for zero measure sets are compound Poisson provided the…
We find conditions for stationary measures of random dynamical systems on surfaces having dissipative diffeomorphisms to be absolutely continuous. These conditions involve a uniformly expanding on average property in the future (UEF) and…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…
We consider conditions for the convergence of sequences in terms of positive and alternating Perron expansions ($P$-representation and $P^-$-representation). These conditions are crucial to determine the continuity of functions that are…