On some properties of transition operators.
On some sample path properties of Skorohod integral processes
On spectral measures of strings and excursions of quasi-diffusions
On spectral type of nonanticipative transformation of Wiener process
On stopped Feynman-Kac functionals
On Strassen's theorem on stochastic domination.
On strong ergodicity of inhomogeneous products of finite stochastic matrices
On strong Markov duals.
On subexponentiality of the Lev́y measure of the inverse local time; with applications to penalizations.
On subordinators, self-similar Markov processes and some factorizations of the exponential variable.
On suprema of Lévy processes and application in risk theory
Let X̂=C−Y where Y is a general one-dimensional Lévy process and C an independent subordinator. Consider the times when a new supremum of X̂ is reached by a jump of the subordinator C. We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and X̂ drifts to −∞, we decompose the absolute supremum of X̂ at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.
On symmetric stable random variables and matrix transposition
On the 2-orthogonal polynomials and the generalized birth and death processes.
On the abstract subordinated exit equation.
On the adaptive control of countable Markov chains
On the analogy between self-gravitating Brownian particles and bacterial populations
We develop the analogy between self-gravitating Brownian particles and bacterial populations. In the high friction limit, the self-gravitating Brownian gas is described by the Smoluchowski-Poisson system. These equations can develop a self-similar collapse leading to a finite time singularity. Coincidentally, the Smoluchowski-Poisson system corresponds to a simplified version of the Keller-Segel model of bacterial populations. In this biological context, it describes the chemotactic aggregation...
On the asymptotic behaviour of increasing self-similar Markov processes.
On the asymptotic events of a Markov chain.
On the asymptotic variance in the central limit theorem for particle filters
Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...
On the asymptotic variance in the central limit theorem for particle filters
Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...