A counterexample for the Markov property of local time for diffusions on graphs
A counterexample for the optimality of Kendall-Cranston coupling.
A counterexample on generalized convolutions
A counterexample related to -weights in martingale theory
A counterexample to the smoothness of the solution to an equation arising in fluid mechanics
We analyze the equation coming from the Eulerian-Lagrangian description of fluids. We discuss a couple of ways to extend this notion to viscous fluids. The main focus of this paper is to discuss the first way, due to Constantin. We show that this description can only work for short times, after which the ``back to coordinates map'' may have no smooth inverse. Then we briefly discuss a second way that uses Brownian motion. We use this to provide a plausibility argument for the global regularity for...
A counting process model of survival of parallel load-sharing system
A system composed from a set of independent and identical parallel units is considered and its resistance (survival) against an increasing load is modelled by a counting process model, in the framework of statistical survival analysis. The objective is to estimate the (nonparametrized) hazard function of the distribution of loads breaking the units of the system (i. e. their breaking strengths), to derive the large sample properties of the estimator, and to propose a goodness-of-fit test. We also...
A coupled Cahn-Hilliard particle system.
A coupling technique for stochastic comparison of functions of Markov processes.
A Cramér type theorem for weighted random variables.
A criterion for transience of multidimensional branching random walk in random environment.
A criterion of asymptotic stability for Markov-Feller e-chains on Polish spaces
Stettner [Bull. Polish Acad. Sci. Math. 42 (1994)] considered the asymptotic stability of Markov-Feller chains, provided the sequence of transition probabilities of the chain converges to an invariant probability measure in the weak sense and converges uniformly with respect to the initial state variable on compact sets. We extend those results to the setting of Polish spaces and relax the original assumptions. Finally, we present a class of Markov-Feller chains with a linear state space model which...
A criterium for the strict positivity of the density of the law of a Poisson process.
A critical function for the planar brownian convex hull
A Decomposition Theorem for Additive Set-Functions, with Applications to Pettis Integrals and Ergodic Means.
A description of stochastic systems using chaotic maps.
A determinant formula from random walks
One usually studies the random walk model of a cat moving from one room to another in an apartment. Imagine now that the cat also has the possibility to go from one apartment to another by crossing some corridors, or even from one building to another. That yields a new probabilistic model for which each corridor connects the entrance rooms of several apartments. This article computes the determinant of the stochastic matrix associated to such random walks. That new model naturally allows to compute...
A deterministic discretisation-step upper bound for state estimation via Clark transformations.
A deterministic displacement theorem for Poisson processes.
A deviation inequality for non-reversible Markov processes
A different construction of gaussian fields from Markov chains : Dirichlet covariances