Large and moderate deviations for the local time of a recurrent Markov chain on
Large deviation estimate of transition densities for jump processes
Large deviation principle of occupation measure for stochastic Burgers equation
Large deviation probabilities for some rescaled superprocesses
Large deviations and full Edgeworth expansions for finite Markov chains with applications to the analysis of genomic sequences
To establish lists of words with unexpected frequencies in long sequences, for instance in a molecular biology context, one needs to quantify the exceptionality of families of word frequencies in random sequences. To this aim, we study large deviation probabilities of multidimensional word counts for Markov and hidden Markov models. More specifically, we compute local Edgeworth expansions of arbitrary degrees for multivariate partial sums of lattice valued functionals of finite Markov...
Large deviations and Nelson processes.
Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes.
Large deviations for local times of stable processes and stable random walks in 1 dimension.
Large deviations for long range interacting particle systems with jumps
Large deviations for the empirical measures of reflecting Brownian motion and related constrained processes in .
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 for voter model occupation times in two dimensions
We study the decay rate of large deviation probabilities of occupation times, up to time t, for the voter model η: ℤ2×[0, ∞)→{0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density ρ∈(0, 1). In [Probab. Theory Related Fields77 (1988) 401–413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(t), log2(t)]. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are log2(t) when...
Large deviations of Markov chains indexed by random trees
Large deviations principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
We establish a Large Deviations Principle for diffusions with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof is based on a viscosity solution approach. The idea consists in interpreting the probabilities as the solutions to some PDEs, make the logarithmic transform, pass to the limit, and then identify the action functional as the solution of the limiting equation.
Large favourite sites of simple random walk and the Wiener process.
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...
Large scale behavior of semiflexible heteropolymers
We consider a general discrete model for heterogeneous semiflexible polymer chains. Both the thermal noise and the inhomogeneous character of the chain (the disorder) are modeled in terms of random rotations. We focus on the quenched regime, i.e., the analysis is performed for a given realization of the disorder. Semiflexible models differ substantially from random walks on short scales, but on large scales a brownian behavior emerges. By exploiting techniques from tensor analysis and non-commutative...
Large scale behaviour of the spatial -Fleming–Viot process
We consider the spatial -Fleming–Viot process model (Electron. J. Probab.15(2010) 162–216) for frequencies of genetic types in a population living in , in the special case in which there are just two types of individuals, labelled and . At time zero, everyone in a given half-space has type 1, whereas everyone in the complementary half-space has type . We are concerned with patterns of frequencies of the two types at large space and time scales. We consider two cases, one in which the dynamics...
Large systems of path-repellent Brownian motions in a trap at positive temperature.
Large volume asymptotics of brownian integrals and orbital magnetism