In this paper we study the Poincaré constant for the Gaussian measure restricted to D = R − B(y, r) where B(y, r) denotes the Euclidean ball with center y and radius r, and d ≥ 2. We also study the case of the l ball (the hypercube). This is the first step in the study of the asymptotic behavior of a d-dimensional Ornstein-Uhlenbeck process in the presence of obstacles with elastic normal refle...

Multivariate Lévy-driven mixed moving average (MMA) processes of the type Xt = ∫ ∫ f(A, t − s)Λ(dA, ds) cover a wide range of well known and extensively used processes such as Ornstein-Uhlenbeck processes, superpositions of Ornstein-Uhlenbeck (supOU) processes, (fractionally integrated) CARMA processes and increments of fractional Lévy processes. In this paper, we introduce multivariate MMA pro...

We propose a generalization of the Ornstein-Uhlenbeck process in 1+1 dimensions which is the product of a temporal Ornstein-Uhlenbeck process with a spatial one and has exponentially decaying autocorrelation. The generalized Langevin equation of the process, the corresponding Fokker-Planck equation, and a discrete integral algorithm for numerical simulation are given. The process is an alternat...