A singular large deviations phenomenon
A strong limit theorem for weighted sums of sequences of negatively dependent random variables.
About the stationary states of vortex systems
Almost sure central limit theorem for a nonstationary Gaussian sequence.
Almost sure path properties of branching diffusion processes
An integro-local theorem applicable on the whole half-axis to the sums of random variables with regularly varying distributions.
Analysis of statistical equilibrium models of geostrophic turbulence.
Annealed deviations of random walk in random scenery
Annealed Lyapounov exponents and large deviations in a poissonian potential. II
Annealed Lyapounov exponents and large deviations in a poissonian potential. I
Applications of sharp large deviations estimates to optimal cooling schedules
Approximation by Poisson law
We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.
Approximations of the brownian rough path with applications to stochastic analysis
Asymptotic analysis for random walks with nonidentically distributed jumps having finite variance.
Asymptotic behavior of moment sequences.
Asymptotic distributions and Berry-Esseen bounds for sums of record values.
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotic expansions of the invariant density of a Markov process with a small parameter
Asymptotic Feynman–Kac formulae for large symmetrised systems of random walks
We study large deviations principles for N random processes on the lattice ℤd with finite time horizon [0, β] under a symmetrised measure where all initial and terminal points are uniformly averaged over random permutations. That is, given a permutation σ of N elements and a vector (x1, …, xN) of N initial points we let the random processes terminate in the points (xσ(1), …, xσ(N)) and then sum over all possible permutations and initial points, weighted with an initial distribution. We prove level-two...