La fonction de Green d'un processus de Galton-Watson
La σ-algèbre asymptotique d'une chaîne de Galton-Watson
LAN and LAMN for systems of interacting diffusions with branching and immigration
Large deviation probabilities for some rescaled superprocesses
Large deviations for transient random walks in random environment on a Galton–Watson tree
Consider a random walk in random environment on a supercritical Galton–Watson tree, and let τn be the hitting time of generation n. The paper presents a large deviation principle for τn/n, both in quenched and annealed cases. Then we investigate the subexponential situation, revealing a polynomial regime similar to the one encountered in one dimension. The paper heavily relies on estimates on the tail distribution of the first regeneration time.
Large deviations of Markov chains indexed by random trees
Large population limit and time behaviour of a stochastic particle model describing an age-structured population
We study a continuous-time discrete population structured by a vector of ages. Individuals reproduce asexually, age and die. The death rate takes interactions into account. Adapting the approach of Fournier and Méléard, we show that in a large population limit, the microscopic process converges to the measure-valued solution of an equation that generalizes the McKendrick-Von Foerster and Gurtin-McCamy PDEs in demography. The large deviations associated with this convergence are studied. The upper-bound...
Law of large numbers for a class of superdiffusions
Law of large numbers for superdiffusions : the non-ergodic case
In previous work of D. Turaev, A. Winter and the author, the Law of Large Numbers for the local mass of certain superdiffusions was proved under an ergodicity assumption. In this paper we go beyond ergodicity, that is we consider cases when the scaling for the expectation of the local mass is not purely exponential. Inter alia, we prove the analog of the Watanabe–Biggins LLN for super-brownian motion.
Lévy processes conditioned on having a large height process
In the present work, we consider spectrally positive Lévy processes not drifting to and we are interested in conditioning these processes to reach arbitrarily large heights (in the sense of the height process associated with ) before hitting . This way we obtain a new conditioning of Lévy processes to stay positive. The (honest) law of this conditioned process (starting at ) is defined as a Doob -transform via a martingale. For Lévy processes with infinite variation paths, this martingale...
Likely path to extinction in simple branching models with large initial population.
Limit distributions for multitype branching processes of -ary search trees
Let be an integer. The so-called-ary search treeis a discrete time Markov chain which is very popular in theoretical computer science, modelling famous algorithms used in searching and sorting. This random process satisfies a well-known phase transition: when , the asymptotic behavior of the process is Gaussian, but for it is no longer Gaussian and a limit of a complex-valued martingale arises. In this paper, we consider the multitype branching process which is the continuous time version...
Limit laws of transient excited random walks on integers
We consider excited random walks (ERWs) on ℤ with a bounded number of i.i.d. cookies per site without the non-negativity assumption on the drifts induced by the cookies. Kosygina and Zerner [15] have shown that when the total expected drift per site, δ, is larger than 1 then ERW is transient to the right and, moreover, for δ>4 under the averaged measure it obeys the Central Limit Theorem. We show that when δ∈(2, 4] the limiting behavior of an appropriately centered and scaled excited random...
Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions.
Limit theorems for discrete-time metapopulation models.
Limit theorems for exceedances of sequence of branching processes.
Limit Theorems for Non-Critical Branching Processes with Continuous State Space
2000 Mathematics Subject Classification: Primary 60J80, Secondary 60G99.In the paper a modification of the branching stochastic process with immigration and with continuous states introduced by Adke S. R. and Gadag V. G. (1995) is considered. Limit theorems for the non-critical processes with or without non-stationary immigration and finite variance are proved. The subcritical case is illustrated with examples.
Limit theorems for one-dimensional transient random walks in Markov environments
Limit Theorems for Regenerative Excursion Processes
This work is supported by Bulgarian NFSI, grant No. MM–704/97The regenerative excursion process Z(t), t = 0, 1, 2, . . . is constructed by two independent sequences X = {Xi , i ≥ 1} and Z = {Ti , (Zi (t), 0 ≤ t < Ti ), i ≥ 1}. For the embedded alternating renewal process, with interarrival times Xi – the time for the installation and Ti – the time for the work, are proved some limit theorems for the spent worktime and the residual worktime, when at least one of the means of Xi and Ti is infinite. ...
Limit theorems for subcritical branching processes in random environment