An Ornstein-Uhlenbeck process is the most basic mean-reversion model and has been used in various fields such as finance and biology. In some instances, reflecting boundary conditions are needed to restrict the state space of this process. We study an Ornstein-Uhlenbeck diffusion process with a reflecting boundary and its application to finance and neuroscience. In the financial application, th...

We extend to infinite dimensions an explicit formula of Chill, Fašangová, Metafune, and Pallara [2] for the optimal angle of analyticity of analytic Ornstein-Uhlenbeck semigroups. The main ingredient is an abstract representation of the Ornstein-Uhlenbeck operator in divergence form.

In this paper we study first passage times of (reflected) Ornstein–Uhlenbeck processes over compound Poisson-type boundaries. In fact, we extend the results of first rendezvous times of (reflected) Brownian motion and compound Poisson-type processes in Perry, Stadje and Zacks (2004) to the (reflected) Ornstein–Uhlenbeck case.

In this short note, the identity in law, which was obtained by P. Salminen [6], between on one hand, the Ornstein-Uhlenbeck process with parameter γ, killed when it reaches 0, and on the other hand, the 3-dimensional radial Ornstein-Uhlenbeck process killed exponentially at rate γ and conditioned to hit 0, is derived from a simple absolute continuity relationship.

We study the Ornstein-Uhlenbeck operator and the Ornstein-Uhlenbeck semigroup in an open convex subset of an infinite dimensional separable Banach space X. This is done by finite dimensional approximation. In particular we prove Logarithmic-Sobolev and Poincaré inequalities, and thanks to these inequalities we deduce spectral properties of the OrnsteinUhlenbeck operator. 2010 Mathematics Subjec...

We introduce the multivariate Ornstein-Uhlenbeck process, solve it analytically, and discuss how it generalizes a vast class of continuous-time and discretetime multivariate processes. Relying on the simple geometrical interpretation of the dynamics of the Ornstein-Uhlenbeck process we introduce cointegration and its relationship to statistical arbitrage. We illustrate an application to swap co...

In this paper we present a review on the extremal behavior of stationary continuous-time processes with emphasis on generalized Ornstein-Uhlenbeck processes. We restrict our attention to heavy-tailed models like heavy-tailed Ornstein-Uhlenbeck processes or continuous-time GARCH processes. The survey includes the tail behavior of the stationary distribution, the tail behavior of the sample maxim...

Ornstein-Uhlenbeck processes driven by general Lévy process are considered in this paper. We derive strongly consistent estimators for the moments of the underlying Lévy process and for the mean reverting parameter of the Ornstein-Uhlenbeck process. Moreover, we prove that the estimators are asymptotically normal. Finally, we test the empirical performance of our estimators in a simulation stud...

We study regularizing properties for transition semigroups related to Ornstein Uhlenbeck processes with values in a Banach space E which is continuously and densely embedded in a real and separable Hilbert space H . Namely we study conditions under which the transition semigroup maps continuous and bounded functions into differentiable functions. Via a Girsanov type theorem such properties exte...