We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the parameters based on a single observation of the path till the time it reaches a distant site, and prove that the estimator is...

In this paper, we establish the dimension-free Harnack inequality on configuration spaces by using the coupling argument. Furthermore, a unified treatment is also used to prove the equivalence between the Harnack inequality on configuration space and that on the corresponding base space under a...

In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by Lévy processes defined on Rd, R+d and bounded C1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in...

We consider the logarithm of the characteristic polynomial of random permutation matrices, evaluated on a finite set of different points. The permutations are chosen with respect to the Ewens distribution on the symmetric group. We show that the behavior at different points is independent in the...

We present a short and self-contained proof of the following result: a random time is an honest time that avoids all stopping times if and only if it coincides with the (last) time of maximum of a nonnegative local martingale with zero terminal value and no jumps while at its running supremum,...

This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to that of the corresponding deterministic delay differential...

We develop a martingale-based decomposition for a general class of quadratic forms of Markov chains, which resembles the well-known Hoeffding decomposition of U-statistics of i.i.d. data up to a reminder term. To illustrate the applicability of our results, we discuss how this decomposition may...

This article deals with adaptive nonparametric estimation for Lévy processes observed at low frequency. For general linear functionals of the Lévy measure, we construct kernel estimators, provide upper risk bounds and derive rates of convergence under regularity assumptions.

This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With...

This paper develops a stochastic integration theory with respect to volatility modulated Lévy-driven Volterra (V MLV) processes. It extends recent results in the literature to allow for stochastic volatility and pure jump processes in the integrator. The new integration operator is based on...