A direct proof of the Ray-Knight theorem
A discrete single server queue with Markovian arrivals and phase type group services.
A Donsker theorem to simulate one-dimensional processes with measurable coefficients
In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these quantities by solving some suitable elliptic PDE problems.
A dozen de Finetti-style results in search of a theory
A duality approach to the genealogies of discrete nonneutral Wright-Fisher models.
A family of integral representations for the brownian variables
A family of L 2-spaces associated to the jumps of a Markov process
Given the (canonical) Markov process associated with a sufficiently general semigroup (P t), we establish a result concerning the uniform completeness of a family of L 2-spaces naturally associated with the jumps of the process. An application of this result is presented.
A family of non-Gaussian martingales with Gaussian marginals.
A fine domination principle for excessive measures.
A finite capacity queue with Markovian arrivals and two servers with group services.
A formula for densities of transition functions
A functional central limit theorem for a class of interacting Markov chain Monte Carlo methods.
A game model referring to the control of independent discrete time stochastic processes
A Gaussian correlation inequality and its applications to small ball probabilities.
A Gaussian oscillator.
A gaussian sheet connected to symmetric Markov chains
A Gauss-Kuzmin theorem for the Rosen fractions
Using the natural extensions for the Rosen maps, we give an infinite-order-chain representation of the sequence of the incomplete quotients of the Rosen fractions. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to solve a variant of Gauss-Kuzmin problem for the above fraction expansion.
A general stochastic target problem with jump diffusion and an application to a hedging problem for large investors.
A generalization of Straube's theorem: existence of absolutely continuous invariant measures for random maps.
A generalization of Ueno's inequality for n-step transition probabilities
We provide a generalization of Ueno's inequality for n-step transition probabilities of Markov chains in a general state space. Our result is relevant to the study of adaptive control problems and approximation problems in the theory of discrete-time Markov decision processes and stochastic games.