Ornstein-Uhlenbeck models are continuous-time processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a multivariate Ornstein-Uhlenbeck model driven by a multivariate regularly varying Lévy process with infinite v...

We analyze in this work the effect of the iterated application of the linear operator that maps a Wiener process onto an OrnsteinUhlenbeck process. The processes obtained after p iterations are called Ornstein-Uhlenbeck processes of order p (denoted OU(p)). Technically our composition of operators is easy to manipulate and its parameters can be computed efficiently because, as we show, in most ...

The first-passage time of a Markov process to a moving barrier is considered as a first-exit time for a vector whose components include the process and the barrier. Thus when the barrier is itself a solution of a differential equation, the theory of first-exit times for multidimensional processes may be used to obtain differential equations for the moments and density of the first-passage time ...

The Boltzmann equation is the traditional framework in which one extends time-dependent mean field classical description of a many-body system to include effect particle-particle collisions an approximate manner. A semiclassical extension this approach quantum systems was suggested by Uehling and Uhlenbeck 1933 for both Fermi Bose statistics, many further developments are known as Boltzmann-Ueh...

We derive a new coupling of the running maximum of an Ornstein–Uhlenbeck process and the running maximum of an explicit i.i.d. sequence. We use this coupling to verify a conjecture of Darling and Erdős (1956).

We prove that the passive scalar field in the Ornstein-Uhlenbeck velocity field with wave-number dependent correlation times converges, in the white-noise limit, to that of Kraichnan’s model with higher spatial regularity.

We investigate the asymptotic properties of the sequential maximum likelihhod estimator of the drift parameter for fractional Ornstein-Uhlenbeck type process satisfying a linear stochastic differential equation driven by fractional Brownian motion.