A bound on the deviation probability for sums of non-negative random variables.
A Cramér type theorem for weighted random variables.
A deviation inequality for non-reversible Markov processes
A generalized mean-reverting equation and applications
Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the...
A Geometric Appraoch to Finite Sample and Large Deviation Properties in Two-Way ANOVA with Spherically Distributed Error Vectors.
A large deviation result for the subcritical Bernoulli percolation
A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices
A log-scale limit theorem for one-dimensional random walks in random environments.
A minimum entropy problem for stationary reversible stochastic spin systems on the infinite lattice
A new large deviation inequality for -statistics of order
A new large deviation inequality for U-statistics of order 2
We prove a new large deviation inequality with applications when projecting a density on a wavelet basis.
A note on Cramer's theorem
A note on large deviations for Wiener chaos
A note on quenched moderate deviations for Sinai’s random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai’s regime. We show that the probability for the particle to be, at time and in a typical environment, at a distance larger than () from its initial position, is .
A note on quenched moderate deviations for Sinai's random walk in random environment
We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time t and in a typical environment, at a distance larger than ta (0<a<1) from its initial position, is exp{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))}.
A note on random walk in random scenery
A note on reinsurance contracts with multiple reinstatements
A note on the exponential convergence rate for products of sums
A PDE approach to certain large deviation problems for systems of parabolic equations
A representation formula for large deviations rate functionals of invariant measures on the one dimensional torus
We consider a generic diffusion on the 1D torus and give a simple representation formula for the large deviation rate functional of its invariant probability measure, in the limit of vanishing noise. Previously, this rate functional had been characterized by M. I. Freidlin and A. D. Wentzell as solution of a rather complex optimization problem. We discuss this last problem in full generality and show that it leads to our formula. We express the rate functional by means of a geometric transformation...