The classical Birkhoff ergodic theorem states that for an ergodic Markov process the limiting
behaviour of the time average of a function (having finite p-th moment, p ≥ 1 p≥ 1, with …

We study the stochastic differential equation d X t= A (X t−) d Z t, X 0= x, where Z t=(Z t (1),…,
Z t (d)) T and Z t (1),…, Z t (d) are independent one-dimensional Lévy processes with …

We propose a new approach to construct the eigenvalue expansion in a weighted Hilbert
space of the solution to the Cauchy problem associated to Gauss–Laguerre invariant …

In this paper, we study the homogenization of a diffusion process with jumps, that is, Feller
process generated by an integro-differential operator. This problem is closely related to the …

This paper examines the stationary distribution of the stochastic Lotka-Volterra model with
infinite delay. Since the solutions of stochastic functional or delay differential equations …

We study a class of R^d-valued continuous strong Markov processes that are generated,
only locally, by an ultra-parabolic operator with coefficients that are regular wrt the intrinsic …

We study the long-time asymptotic behaviour of semigroups generated by non-local
Schrödinger operators of the form H=− L+ V; the free operator L is the generator of a …

arXiv:1510.04569v2 [math.PR] 15 Nov 2015 Page 1 arXiv:1510.04569v2 [math.PR] 15 Nov
2015 Scale invariant boundary Harnack principle at infinity for Feller processes Panki Kim∗ …

This paper is concerned with the characterization and the propagation of errors associated
with data limitations in polynomial-chaos-based stochastic methods for uncertainty …

In this paper, as a main result, we derive a Chung-Fuchs type condition for the recurrence of
Feller processes associated with pseudo-differential operators. In the Lévy process case …