Self-similar and Markov composition structures.
Sharp edge, vertex, and mixed Cheeger inequalities for finite Markov kernels.
Sharp large deviations estimates for simulated annealing algorithms
Simple Markov chains
Singles in a Markov chain.
Small perturbation of diffusions in inhomogeneous media
Soft local times and decoupling of random interlacements
In this paper we establish a decoupling feature of the random interlacement process at level , . Roughly speaking, we show that observations of restricted to two disjoint subsets and of are approximately independent, once we add a sprinkling to the process by slightly increasing the parameter . Our results differ from previous ones in that we allow the mutual distance between the sets and to be much smaller than their diameters. We then provide an important application of this...
Sojourn time in ℤ+ for the Bernoulli random walk on ℤ
Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci. USA 35 (1949) 605–608], simpler representations may be obtained...
Sojourn time in ℤ+ for the Bernoulli random walk on ℤ
Let (Sk)k≥1 be the classical Bernoulli random walk on the integer line with jump parameters p ∈ (0,1) and q = 1 − p. The probability distribution of the sojourn time of the walk in the set of non-negative integers up to a fixed time is well-known, but its expression is not simple. By modifying slightly this sojourn time through a particular counting process of the zeros of the walk as done by Chung & Feller [Proc. Nat. Acad. Sci....
Some asymptotic results on extended sequences connected with the regular continued fraction.
Some limit properties of random transition probability for second-order nonhomogeneous Markov chains indexed by a tree.
Some limit theorems for ratios of transition probabilities.
Some Shannon-McMillan approximation theorems for Markov chain field on the generalized Bethe tree.
Stability estimating in optimal stopping problem
We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space . It is supposed that an unknown transition probability , , is approximated by the transition probability , , and the stopping rule , optimal for , is applied to the process governed by . We found an upper bound for the difference between the total expected cost, resulting when applying , and the minimal total expected cost. The bound given is a constant times , where is the total variation...
Stationary measures and phase transition for a class of probabilistic cellular automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Stationary measures and phase transition for a class of Probabilistic Cellular Automata
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Stationary random graphs with prescribed iid degrees on a spatial Poisson process.
Stochastic vortices in periodically reclassified populations
Our paper considers open populations with arrivals and departures whose elements are subject to periodic reclassifications. These populations will be divided into a finite number of sub-populations. Assuming that: a) entries, reclassifications and departures occur at the beginning of the time units; b) elements are reallocated at equally spaced times; c) numbers of new elements entering at the beginning of the time units are realizations...
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 Laws of Large Numbers for Random Walks Associated with a Class of One-Dimensional Convolution Structures.