Consider an Ornstein–Uhlenbeck process with reflection at the origin. Such a process arises as an approximating process both for queueing systems with reneging or state-dependent balking and for multiserver loss models. Consequently, it becomes important to understand its basic properties. In this paper, we show that both the steady-state and transient behavior of the reflected Ornstein–Uhlenbe...

In this paper, we consider the stationary density function of the doubly skew Ornstein-Uhlenbeck process. We present the explicit formula for the stationary density function and show that this process is positive Harris recurrent and geometrically ergodic. We expand our method to the more general cases in which the multiple parameters are present and we try to consider the stability of the skew...

Skew convolution semigroups play an important role in the study of generalized Mehler semigroups and Ornstein-Uhlenbeck processes. We give a characterization for a general skew convolution semigroup on real separable Hilbert space whose characteristic functional is not necessarily differentiable at the initial time. A connection between this subject and catalytic branching superprocesses is est...

Abstract We prove asymptotically efficient inference results concerning an Ornstein–Uhlenbeck regression model driven by a non-Gaussian stable Lévy process, where the output process is observed at high frequency over fixed period. The local asymptotics of non-ergodic type for likelihood function presented, followed way to construct estimator through suboptimal, yet very simple preliminary estim...

The classical Ornstein-Uhlenbeck diffusion neuronal model is generalized by inclusion of a time-dependent input whose strength exponentially decreases in time. The behavior of the membrane potential is consequently seen to be modeled by a process whose mean and covariance classify, it as Gaussian-Markov. The effect of the input on the neuron's firing characteristics is investigated by comparing...

We consider the nonlinear filtering model with Ornstein-Uhlenbeck process as noise and obtain an analogue of the Bayes’ formula for the filter. For this we need to consider a modified model, where the instaneteneous effect h(Xt) of the signal in the usual model is replaced by ξ t = α ∫ t (t− 1 α )∨0 h(Xu) du, (where α is a large parameter). This means that there is a lingering effect of the sig...

This paper uses linear programming to numerically evaluate the Laplace transform of the exit time distribution and the resolvent of the moments of various Markov processes in bounded regions. The linear programming formulation is developed from a martingale characterization of the processes and the use of occupation measures. The LP approach naturally provides both upper and lower bounds on the...

The Ornstein-Uhlenbeck semigroup combines Gaussian diffusion with the flow of a linear vector field. In infinite dimensional settings there can be non-Gaussian invariant measures. This gives a context for one version of the renormalization group. The adjoint of the OrnsteinUhlenbeck semigroup with respect to an invariant measure need not be an Ornstein-Uhlenbeck semigroup. This adjoint is the a...

Using positive semidefinite processes of Ornstein-Uhlenbeck type a multivariate Ornstein-Uhlenbeck (OU) type stochastic volatility model is introduced. We derive many important statistical and probabilistic properties, e.g. the complete second order structure and a state-space representation. Noteworthy, many of our results are shown to be valid for the more general class of multivariate stocha...