Inefficient estimators of the bivariate survival function for three models
Invariance principle for Mott variable range hopping and other walks on point processes
We consider a random walk on a homogeneous Poisson point process with energy marks. The jump rates decay exponentially in the -power of the jump length and depend on the energy marks via a Boltzmann-like factor. The case corresponds to the phonon-induced Mott variable range hopping in disordered solids in the regime of strong Anderson localization. We prove that for almost every realization of the marked process, the diffusively rescaled random walk, with an arbitrary start point, converges to...
Invariance principle for the random conductance model with dynamic bounded conductances
We study a continuous time random walk in an environment of dynamic random conductances in . We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for , and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.
Invariance principle in a bilinear model with weak nonlinearity.
Invariance principle, multifractional gaussian processes and long-range dependence
This paper is devoted to establish an invariance principle where the limit process is a multifractional gaussian process with a multifractional function which takes its values in (1/2, 1). Some properties, such as regularity and local self-similarity of this process are studied. Moreover the limit process is compared to the multifractional brownian motion.
Invariance principles for absolutely regular empirical processes
Invariance principles for Brownian intersection local time and polymer measures.
Invariance Principles for Martingales and Sums of Indpendent Random Variables.
Invariance principles for random walks conditioned to stay positive
Let {Snbe a random walk in the domain of attraction of a stable law , i.e. there exists a sequence of positive real numbers ( an) such that Sn/anconverges in law to . Our main result is that the rescaled process (S⌊nt⌋/an, t≥0), when conditioned to stay positive, converges in law (in the functional sense) towards the corresponding stable Lévy process conditioned to stay positive. Under some additional assumptions, we also prove a related invariance principle for the random walk killed at its first...
Invariance principles for ranked excursion lengths and heights.
Invariance principles for spatial multitype Galton–Watson trees
We prove that critical multitype Galton–Watson trees converge after rescaling to the brownian continuum random tree, under the hypothesis that the offspring distribution is irreducible and has finite covariance matrices. Our study relies on an ancestral decomposition for marked multitype trees, and an induction on the number of types. We then couple the genealogical structure with a spatial motion, whose step distribution may depend on the structure of the tree in a local way, and show that the...
Invariance principles in Hölder spaces.
Invariance principles in