A central limit theorem for random walks in random labyrinths
A central limit theorem for two-dimensional random walks in a cone
We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only if the tail distribution of the exit time from the cone is regularly varying. This condition is satisfied in many natural examples.
A functional central limit theorem for a class of interacting Markov chain Monte Carlo methods.
A functional central limit theorem for martingales in C(K) and its application to sequential estimates.
A functional combinatorial central limit theorem.
A functional hungarian construction for sums of independent random variables
A functional limit theorem for a 2D-random walk with dependent marginals.
A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables.
A limit theorem for the position of a particle in the Lorentz model.
A limit theorem for the Riemann zeta-function in the complex space
A non-Skorokhod topology on the Skorokhod space.
A Note Invariance Principles for v. Mises'-Statistics.
A note on the invariance principle of the product of sums of random variables.
A quenched weak invariance principle
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.
A strong invariance principle for negatively associated random fields
In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite th moment and the covariance coefficient exponentially decreases to . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.
A strong invariance theorem for the tail empirical process
About increments of additive functionals of diffusion processes.
Almost sure functional central limit theorem for ballistic random walk in random environment
We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central limit theorem, under almost every environment for the diffusively scaled centered walk. The main point behind the invariance principle is that the quenched mean of the walk behaves subdiffusively.
Almost sure functional limit theorem for the product of partial sums
We prove an almost sure functional limit theorem for the product of partial sums of i.i.d. positive random variables with finite second moment.
Almost sure functional limit theorems in .