Poisson approximation for sums of dependent Bernoulli random variables.
Poisson Approximation for the Number of Large Digits of Inhomogeneous f-Expansions.
Poisson perturbations
Poisson perturbations
Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Čekanavičius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent random variables. ...
Precise lim sup behavior of probabilities of large deviations for sums of i.i.d. random variables.
Precise rates in log laws for NA sequences.
Predictability, entropy and information of infinite transformations
We show that a certain type of quasifinite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasifinite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with normalization ∝ √n. Lastly, we show that certain ergodic, probability preserving...
Probabilistic representations of operator semigroups - A unifying approach.
Process level moderate deviations for stabilizing functionals
Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including...
Processus de zéro-rangé avec particule marquée
Product of exponentials and spectral radius of random k-circulants
We consider n × n random k-circulant matrices with n → ∞ and k = k(n) whose input sequence {al}l≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + δ) moment. We study the asymptotic distribution of the spectral radius, when n = kg + 1. For this, we first derive the tail behaviour of the g fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we show that with appropriate scaling...
Projecting the surface measure of the sphere of
Quadratic variations and estimation of the local Hölder index of a gaussian process
Quantitative recurrence in two-dimensional extended processes
Under some mild condition, a random walk in the plane is recurrent. In particular each trajectory is dense, and a natural question is how much time one needs to approach a given small neighbourhood of the origin. We address this question in the case of some extended dynamical systems similar to planar random walks, including ℤ2-extension of mixing subshifts of finite type. We define a pointwise recurrence rate and relate it to the dimension of the process, and establish a result of convergence in...
Quantum limit theorems
A noncommutative analogue of limit theorems in classical probability theory for distributions of canonical pairs of observables is considered. A complete description of all limit probability operators which are quantum counterparts of the classical infinitely divisible and semistable laws is obtained in the case when scalar norming is generalised to norming by 2 × 2 matrices.
Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct.
Quelques propriétés de certaines marches aléatoires en milieu aléatoire
Quenched limits for transient, ballistic, sub-gaussian one-dimensional random walk in random environment
We consider a nearest-neighbor, one-dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient with speed vP>0 and there exists an s∈(1, 2) such that the annealed law of n−1/s(Xn−nvP) converges to a stable law of parameter s. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible. In particular we show that there exist sequences {tk} and {tk'} depending on the environment only, such that a quenched...
Random evolutions processes induced by discrete time Markov chains.
Random recursive trees and the Bolthausen-Sznitman coalescent.