We study a long-range dependence Gaussian process which we call “sub-fractional Brownian motion” (sub-fBm), because it is intermediate between Brownian motion (Bm) and fractional Brownian motion… (More)

We consider particle systems in locally compact Abelian groups with particles moving according to a process with symmetric stationary independent increments and undergoing one and two levels of… (More)

The notion of degree and related notions concerning recurrence and transience for a class of Lévy processes on metric Abelian groups are studied. The case of random walks on a hierarchical group is… (More)

We study asymptotic percolation as N → ∞ in an infinite random graph GN embedded in the hierarchical group of order N , with connection probabilities depending on an ultrametric distance between… (More)

For a random element X of a nuclear space of distributions on Wiener space C([0, 1],R), the localization problem consists in “projecting” X at each time t ∈ [0, 1] in order to define an S ′(R)-valued… (More)

We extend results on time-rescaled occupation time fluctuation limits of the (d, α, β)-branching particle system (0 < α ≤ 2, 0 < β ≤ 1) with Poisson initial condition. The earlier results in the… (More)

We consider a class of mulfitype particle systems in R d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe… (More)

The (d, α, β, γ)-branching particle system consists of particles moving in R according to a symmetric α-stable Lévy process (0 < α ≤ 2), splitting with a critical (1 + β)-branching law (0 < β ≤ 1),… (More)

We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, α, β)-branching particle system (particles moving in R d according to a symmetric α-stable Lévy process,… (More)

The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group ΩN consisting of families of individuals undergoing critical branching random walk and… (More)