Sample path large deviations principles for Poisson shot noise processes, and applications.
Scaling of a random walk on a supercritical contact process
We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...
Self-normalized large deviations for Markov chains.
Sharp estimates of deviations of the sample mean in many dimensions
Sharp large deviations estimates for simulated annealing algorithms
Sharp large deviations for gaussian quadratic forms with applications
Sharp large deviations for Gaussian quadratic forms with applications
Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process, and finally of the empirical...
Slowdown estimates for ballistic random walk in random environment
We consider models of random walk in uniformly elliptic i.i.d. random environment in dimension greater than or equal to 4, satisfying a condition slightly weaker than the ballisticity condition . We show that for every and large enough, the annealed probability of linear slowdown is bounded from above by . This bound almost matches the known lower bound of , and significantly improves previously known upper bounds. As a corollary we provide almost sharp estimates for the quenched probability...
Small deviation probabilities for a class of distributions with a polynomial decreasing at zero.
Small deviations of iterated processes in the space of trajectories
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different.
Small diffusion and fast dying out asymptotics for superprocesses as non-Hamiltonian quasiclassics for evolution equations.
Small positive values for supercritical branching processes in random environment
Branching Processes in Random Environment (BPREs) are the generalization of Galton–Watson processes where in each generation the reproduction law is picked randomly in an i.i.d. manner. In the supercritical case, the process survives with positive probability and then almost surely grows geometrically. This paper focuses on rare events when the process takes positive but small values for large times. We describe the asymptotic behavior of , as . More precisely, we characterize the exponential...
Solutions of stochastic differential equations obeying the law of the iterated logarithm, with applications to financial markets.
Some results on convergence rates for probabilities of moderate deviations for sums of random variables.
Stability of precise Laplace's method under approximations; Applications
We study the fluctuations around non degenerate attractors of the empirical measure under mean field Gibbs measures. We prove that a mild change of the densities of these measures does not affect the central limit theorems. We apply this result to generalize the assumptions of [3] and [12] on the densities of the Gibbs measures to get precise Laplace estimates.
Stability of precise Laplace's method under approximations ; applications
Statistics of return times for weighted maps of the interval
Stochastic nonlinear Schrödinger equations driven by a fractional noise, well-posedness, large deviations and support.
Stone-Weierstrass type theorems for large deviations.
Subexponential tail asymptotics for a random walk with randomly placed one-way nodes