Asymptotics of a dynamic random walk in a random scenery : I. Law of large numbers
Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks.
Asymptotics of riskless profit under selling of discrete time call options
A discrete time model of financial market is considered. In the focus of attention is the guaranteed profit of the investor which arises when the jumps of the stock price are bounded. The limit distribution of the profit as the model becomes closer to the classic model of geometrical Brownian motion is established. It is of interest that the approximating continuous time model does not assume any such profit.
Asymptotics of the stationary distribution of an oscillating random walk.
Average properties of random walks on Galton-Watson trees
Averages of unitary representations and weak mixing of random walks
Let S be a locally compact (σ-compact) group or semigroup, and let T(t) be a continuous representation of S by contractions in a Banach space X. For a regular probability μ on S, we study the convergence of the powers of the μ-average Ux = ʃ T(t)xdμ(t). Our main results for random walks on a group G are: (i) The following are equivalent for an adapted regular probability on G: μ is strictly aperiodic; converges weakly for every continuous unitary representation of G; U is weakly mixing for any...
Barycentres de matrices idempotentes stochastiques
Block distribution in random strings
For almost all infinite binary sequences of Bernoulli trials the frequency of blocks of length in the first terms tends asymptotically to the probability of the blocks, if increases like (for ) where tends to . This generalizes a result due to P. Flajolet, P. Kirschenhofer and R.F. Tichy concerning the case .
Bornes inférieures pour les marches aléatoires sur les groupes p-adiques moyennables
Bounds on random infinite urn model.
Branching random walks on binary search trees: convergence of the occupation measure
We consider branching random walks with binary search trees as underlying trees. We show that the occupation measure of the branching random walk, up to some scaling factors, converges weakly to a deterministic measure. The limit depends on the stable law whose domain of attraction contains the law of the increments. The existence of such stable law is our fundamental hypothesis. As a consequence, using a one-to-one correspondence between binary trees and plane trees, we give a description of the...
Brownian local times.
Brownian motion and random walks on manifolds
We develop a procedure that allows us to “descretise” the Brownian motion on a Riemannian manifold. We construct thus a random walk that is a good approximation of the Brownian motion.
Brownian motion and transient groups
In this paper I consider a covering of a Riemannian manifold . I prove that Green’s function exists on if any and only if the symmetric translation invariant random walks on the covering group are transient (under the assumption that is compact).
Brownian motion, bridge excursion, and meander characterized by sampling at independent uniform times.
Capacité et théorie du renouvellement. I
Caractérisation des groupes de Lie connexes récurrents
Caractérisation des groupes localement compacts de type (T) ayant la propriété de point fixe
Cauchy approximation for sums of independent random variables.
Central limit theorem for Hölder processes on -unit cube
We consider a sequence of stochastic processes with continuous trajectories and we show conditions for the tightness of the sequence in the Hölder space with a parameter .