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...

In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some canonical rational morphisms among the Gieseker compactifications are proved to exist and their fibers are studied. As a consequence of studying the morphisms from the Gieseker compactifications to the Uh...

Taking full advantage of two independent projectively equivalent metrics on the ellipsoid leading to Liouville integrability of the geodesic flow via the well-known Jacobi-Moser system, we disclose a novel integrable system on the sphere S, namely the dual Moser system. The latter falls, along with the Jacobi-Moser and Neumann-Uhlenbeck systems, into the category of (locally) Stäckel systems. M...

De Haan and Karandikar [12] introduced generalized Ornstein–Uhlenbeck processes as one-dimensional processes (Vt)t≥0 which are basically characterized by the fact that for each h > 0 the equidistantly sampled process (Vnh)n∈N0 satisfies the random recurrence equation Vnh = A(n−1)h,nhV(n−1)h + B(n−1)h,nh, n ∈ N, where (A(n−1)h,nh, B(n−1)h,nh)n∈N is an i.i.d. sequence with positive A0,h for each ...

In this paper we consider an Ornstein-Uhlenbeck (ou) process (M(t))t>0 whose parameters are determined by an external Markov process (X(t))t>0 on a nite state space {1, . . . , d}; this process is usually referred to as Markov-modulated Ornstein-Uhlenbeck (or: mmou). We use stochastic integration theory to determine explicit expressions for the mean and variance of M(t). Then we establish a sys...

Langevin-like equations have been studied in the presence of arbitrary noise. The characteristic functional of the generalized Langevin process has been built up. Exact results for all cumulants are given. Particular stress has been put on the Campbell, dichotomous and radioactive decay noises. Transient relaxation, susceptibility and diffusion constants for different (noisy) media have been sk...

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...