Schwach irreduzible Markoff-Operatoren.
Séries rationnelles positives et processus stochastiques
Singularities of the Green Function of a Random Walk on a Discrete Group.
Skorokhod stopping in discrete time
Small perturbation of diffusions in inhomogeneous media
Small positive values for supercritical branching processes in random environment
Branching Processes in Random Environment (BPREs) are the generalization of Galton–Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical case, the process survives with positive probability and then almost surely grows geometrically. This paper focuses on rare events when the process takes positive but small values for large times. We describe the asymptotic behavior of , as . More precisely, we characterize the exponential...
Solution to the optimality equation in a class of Markov decision chains with the average cost criterion
Some notes on topological recurrence.
Stability of iterates of Markov operators
Stability of Markov processes nonhomogeneous in time
We study the asymptotic behaviour of discrete time processes which are products of time dependent transformations defined on a complete metric space. Our sufficient condition is applied to products of Markov operators corresponding to stochastically perturbed dynamical systems and fractals.
Stochastic differential equation driven by a pure-birth process
A generalization of the Poisson driven stochastic differential equation is considered. A sufficient condition for asymptotic stability of a discrete time-nonhomogeneous Markov process is proved.
Stochastic dynamical systems with weak contractivity properties II. Iteration of Lipschitz mappings
In this continuation of the preceding paper (Part I), we consider a sequence of i.i.d. random Lipschitz mappings → , where is a proper metric space. We investigate existence and uniqueness of invariant measures, as well as recurrence and ergodicity of the induced stochastic dynamical system (SDS) starting at x ∈ . The main results concern the case when the associated Lipschitz constants are log-centered. Principal tools are local contractivity, as considered in detail in Part I, the Chacon-Ornstein...
Stochastic dynamical systems with weak contractivity properties I. Strong and local contractivity
Consider a proper metric space and a sequence of i.i.d. random continuous mappings → . It induces the stochastic dynamical system (SDS) starting at x ∈ . In this and the subsequent paper, we study existence and uniqueness of invariant measures, as well as recurrence and ergodicity of this process. In the present first part, we elaborate, improve and complete the unpublished work of Martin Benda on local contractivity, which merits publicity and provides an important tool for studying stochastic...
Stopping Markov processes and first path on graphs
Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a noncombinatorial manner to compute the law of a first given path among a set of stopping paths.We prove the existence of a minimal Markov chain without oversized information....
Strong and weak stability of some Markov operators
An integral Markov operator appearing in biomathematics is investigated. This operator acts on the space of probabilistic Borel measures. Let and be probabilistic Borel measures. Sufficient conditions for weak and strong convergence of the sequence to are given.
Structure of mixing and category of complete mixing for stochastic operators
Let T be a stochastic operator on a σ-finite standard measure space with an equivalent σ-finite infinite subinvariant measure λ. Then T possesses a natural "conservative deterministic factor" Φ which is the Frobenius-Perron operator of an invertible measure preserving transformation φ. Moreover, T is mixing ("sweeping") iff φ is a mixing transformation. Some stronger versions of mixing are also discussed. In particular, a notion of *L¹-s.o.t. mixing is introduced and characterized in terms of weak...
Sur la frontière de Martin des processus de Markov à temps discret
Sur le maximum d'un processus aléatoire.
Sur les opérateurs multiplicativement liés
Sur l'orthogonalité de deux lois de probabilités correspondant à deux processus de Markov