Existence of a critical point for the infinite divisibility of squares of Gaussian vectors in with non-zero mean.
Existence of moments of increasing predictable processes associated with one- and two-parameter potentials.
Existence of nontrivial stochastic monoids.
Existence of positive harmonic functions on groups and on covering manifolds
Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure.
Expansion and random walks in : I
We prove that the Cayley graphs of are expanders with respect to the projection of any fixed elements in generating a Zariski dense subgroup.
Expansion and random walks in : II
Expansions for Gaussian processes and Parseval frames.
Expectation, conditional expectation and martingales in local fields.
Expected number of real zeros of Lévy and harmonizable stable random polynomials.
Explicit Karhunen-Loève expansions related to the Green function of the Laplacian
Karhunen-Loève expansions of Gaussian processes have numerous applications in Probability and Statistics. Unfortunately the set of Gaussian processes with explicitly known spectrum and eigenfunctions is narrow. An interpretation of three historical examples enables us to understand the key role of the Laplacian. This allows us to extend the set of Gaussian processes for which a very explicit Karhunen-Loève expansion can be derived.
Explicit solutions of some fractional partial differential equations via stable subordinators.
Explosion time in stochastic differential equations with small diffusion.
Exponential approximation for hitting times in mixing processes.
Exponential asymptotics for intersection local times of stable processes and random walks
Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces
We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by Lévy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of convergence in the norm of total variation. Our general result is applied to a number of specific equations driven by cylindrical symmetric α-stable noise and/or cylindrical Wiener noise. We also consider the case of a "singular" Wiener process with unbounded covariance...
Exponential functionals of Lev́y processes.
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients....
Exponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. ...
Exponential inequalities for self-normalized processes with applications.