Conditional limit theorems for ordered random walks.
Continuous Ocone martingales as weak limits of rescaled martingales.
Contre-exemple dans le théorème central limite fonctionnel pour les champs aléatoires réels
Convergence and convergence rate to fractional Brownian motion for weighted random sums.
Convergence des surmartingales. Application aux vraisemblances partielles
Convergence faible et principe d'invariance pour des martingales à valeurs dans des espaces de Sobolev
Convergence for step line processes under summation of random indicators and models of market pricing.
Convergence of Submartingales to an Increasing Process under Discretization of Filtrations
Convergence pour les processus empiriques éclatés
Convergence results and sharp estimates for the voter model interfaces.
Convergence to the brownian Web for a generalization of the drainage network model
We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing paths that can cross each other and are dependent even before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.
Covariance inequalities for strongly mixing processes
Diffusion in long-range correlated Ornstein-Uhlenbeck flows.
Dynamical attraction to stable processes
We apply dynamical ideas within probability theory, proving an almost-sure invariance principle in log density for stable processes. The familiar scaling property (self-similarity) of the stable process has a stronger expression, that the scaling flow on Skorokhod path space is a Bernoulli flow. We prove that typical paths of a random walk with i.i.d. increments in the domain of attraction of a stable law can be paired with paths of a stable process so that, after applying a non-random regularly...
Erratum to “Number variance from a probabilistic perspective, infinite systems of independent Brownian motions and symmetric -stable processes".
Estimates in the invariance principle in terms of truncated power moments.
Estimates of the rate of approximation in a de-poissonization lemma
Euler's Approximations of Solutions of Reflecting SDEs with Discontinuous Coefficients
Let D be either a convex domain in or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman (1984) and Saisho (1987). We investigate convergence in law as well as in for the Euler and Euler-Peano schemes for stochastic differential equations in D with normal reflection at the boundary. The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure, and the diffusion coefficient may degenerate on some subsets of the domain.
Euler's Approximations of Weak Solutions of Reflecting SDEs with Discontinuous Coefficients
We study convergence in law for the Euler and Euler-Peano schemes for stochastic differential equations reflecting on the boundary of a general convex domain. We assume that the coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. The proofs are based on new estimates of Krylov's type for the approximations considered.
Existence and spatial limit theorems for lattice and continuum particle systems.