On the left endpoints of brownian excursions
On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case
Under a well-known scaling, supercritical Galton–Watson processes Z converge to a non-degenerate non-negative random limit variable W. We are dealing with the left tail (i.e. close to the origin) asymptotics of its law. In the Böttcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the Böttcher case, we improve a recent lower deviation...
On the lengths of excursions of some Markov processes
On the level crossing of multi-dimensional delayed renewal processes.
On the Lévy transformation of brownian motions and continuous martingales
On the Levy-Chintschin formula on locally compact maximally almost periodic groups.
On the limit behaviour of sums of a random number of independent random variables
On the limit distribution of the well-distribution measure of random binary sequences
We prove the existence of a limit distribution of the normalized well-distribution measure (as ) for random binary sequences , by this means solving a problem posed by Alon, Kohayakawa, Mauduit, Moreira and Rödl.
On the limit distributions of kth order statistics for semi-pareto processes
Asymptotic properties of the kth largest values for semi-Pareto processes are investigated. Conditions for convergence in distribution of the kth largest values are given. The obtained limit laws are represented in terms of a compound Poisson distribution.
On the limiting behavior of a harmonic oscillator with random external disturbance.
On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution
We consider n × n real symmetric and hermitian random matrices Hₙ that are sums of a non-random matrix and of mₙ rank-one matrices determined by i.i.d. isotropic random vectors with log-concave probability law and real amplitudes. This is an analog of the setting of Marchenko and Pastur [Mat. Sb. 72 (1967)]. We prove that if mₙ/n → c ∈ [0,∞) as n → ∞, and the distribution of eigenvalues of and the distribution of amplitudes converge weakly, then the distribution of eigenvalues of Hₙ converges...
On the limiting velocity of random walks in mixing random environment
We consider random walks in strong-mixing random Gibbsian environments in , . Based on regeneration arguments, we will first provide an alternative proof of Rassoul-Agha’s conditional law of large numbers (CLLN) for mixing environment (Electron. Commun. Probab.10(2005) 36–44). Then, using coupling techniques, we show that there is at most one nonzero limiting velocity in high dimensions ().
On the Linear Combinations of Stochastic Variables.
On the linear prediction problem of certain non-stationary stochastic processes.
On the local limit theorem for general lattice distribution.
On the local time density of the reflecting Brownian bridge.
On the local time of sub-fractional Brownian motion
be a sub-fractional Brownian motion with . We establish the existence, the joint continuity and the Hölder regularity of the local time of . We will also give Chung’s form of the law of iterated logarithm for . This results are obtained with the decomposition of the sub-fractional Brownian motion into the sum of fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. This decomposition is given by Ruiz de Chavez and Tudor [10].
On the long-time behaviour of a class of parabolic SPDE’s : monotonicity methods and exchange of stability
In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear parabolic stochastic partial differential equations driven by a standard multidimensional brownian motion. We first use monotonicity methods to prove that the random fields either stabilize exponentially rapidly with probability one around one of the two equilibrium states, or that they set out to oscillate between them. In the first case we can...
On the long-time behaviour of a class of parabolic SPDE's: monotonicity methods and exchange of stability
In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear parabolic stochastic partial differential equations driven by a standard multidimensional Brownian motion. We first use monotonicity methods to prove that the random fields either stabilize exponentially rapidly with probability one around one of the two equilibrium states, or that they set out to oscillate between them. In the first case we can...
On the lower bound for the number of real roots of a random algebraic equation.