Related papers: Ornstein-Uhlenbeck processes of bounded variation
Even in a simple stochastic process, the study of the full distribution of time integrated observables can be a difficult task. This is the case of a much-studied process such as the Ornstein-Uhlenbeck process where, recently, anomalous…
Fractional Ornstein-Uhlenbeck process of the second kind $(\text{fOU}_{2})$ is solution of the Langevin equation $\mathrm{d}X_t = -\theta X_t\,\mathrm{d}t+\mathrm{d}Y_t^{(1)}, \ \theta >0$ with Gaussian driving noise $ Y_t^{(1)} := \int^t_0…
The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on L\'evy driven Ornstein-Uhlenbeck (OU) type processes. Discrete superpositions of these processes can be…
We study the strong consistency and asymptotic normality of a least squares estimator of the drift coefficient in complex-valued Ornstein-Uhlenbeck processes driven by fractional Brownian motion, extending the results of Chen, Hu, Wang…
We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such process we specify mean and…
We characterise the nonequilibrium stationary state of a generic multivariate Ornstein-Uhlenbeck process involving $N$ degrees of freedom. The irreversibility of the process is encoded in the antisymmetric part of the Onsager matrix. The…
The indefinite integral of the homogenized Ornstein-Uhlenbeck process is a well-known model for physical Brownian motion, modelling the behaviour of an object subject to random impulses [L. S. Ornstein, G. E. Uhlenbeck: On the theory of…
SupOU processes are superpositions of Ornstein-Uhlenbeck type processes with a random intensity parameter. They are stationary processes whose marginal distribution and dependence structure can be specified independently. Integrated supOU…
We combine earlier investigations of linear systems with L\'{e}vy fluctuations [Physica {\bf 113A}, 203, (1982)] with recent discussions of L\'{e}vy flights in external force fields [Phys.Rev. {\bf E 59},2736, (1999)]. We give a complete…
Veestraeten [1] recently derived inverse Laplace transforms for Laplace transforms that contain products of two parabolic cylinder functions by exploiting the link between the parabolic cylinder function and the transition density and…
We consider a branching particle system consisting of particles moving according to the Ornstein-Uhlenbeck process in $\Rd$ and undergoing a binary, supercritical branching with a constant rate $\lambda>0$. This system is known to fulfil a…
For an arbitrary Hilbert space-valued Ornstein-Uhlenbeck process we construct the Ornstein-Uhlenbeck Bridge connecting a starting point $x$ and an endpoint $y$ that belongs to a certain linear subspace of full measure. We derive also a…
In this paper, we consider an ergodic Ornstein-Uhlenbeck process with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its jump intensity depend on unknown parameters.…
The first-passage problem of the Ornstein-Uhlenbeck process to a boundary is a long-standing problem with no known closed-form solution except in specific cases. Taking this as a starting-point, and extending to a general mean-reverting…
The question of existence and properties of stationary solutions to Langevin equations driven by noise processes with stationary increments is discussed, with particular focus on noise processes of pseudo-moving-average type. On account of…
Based on an integration by parts formula for closed and convex subsets $\Gamma$ of a separable real Hilbert space $H$ with respect to a Gaussian measure, we first construct and identify the infinite dimensional analogue of the obliquely…
We derive an explicit representation for the transition law of a $p$-tempered $\alpha$-stable process of Ornstein-Uhlenbeck-type and use it to develop a methodology for simulation. Our results apply in both the univariate and multivariate…
The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional…
This work concerns the Ornstein-Uhlenbeck type process associated to a positive self-similar Markov process $(X(t))_{t\geq 0}$ which drifts to $\infty$, namely $U(t):= {\rm e}^{-t}X({\rm e}^t-1)$. We point out that $U$ is always a…
We consider an ensemble of Ornstein-Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass like variable…