Related papers: Absolute Continuity under Time Shift for Ornstein-…

The paper is concerned with a class of two-sided stochastic processes of the form $X=W+A$. Here $W$ is a two-sided Brownian motion with random initial data at time zero and $A\equiv A(W)$ is a function of $W$. Elements of the related…

We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small…

Let $X$ be a $n$-dimensional Ornstein-Uhlenbeck process, solution of the S.D.E. $$\d X_t = AX_t \d t + \d B_t$$ where $A$ is a real $n\times n$ matrix and $B$ a L\'evy process without Gaussian part. We show that when $A$ is non-singular,…

We consider an Ornstein-Uhlenbeck process with values in R^n driven by a L\'evy process (Z_t) taking values in R^d with d possibly smaller than n. The L\'evy noise can have a degenerate or even vanishing Gaussian component. Under a…

In this paper, we study the Ornstein-Uhlenbeck bridge process (i.e. the Ornstein-Uhlenbeck process conditioned to start and end at fixed points) constraints to have a fixed area under its path. We present both anticipative (in this case, we…

We consider a perturbation of a Hilbert space-valued Ornstein--Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls…

In this paper we study some convergence results concerning the one-dimensional distribution of a time-changed fractional Ornstein-Uhlenbeck process. In particular, we establish that, despite the time change, the process admits a Gaussian…

We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…

The Ornstein-Uhlenbeck process is interpreted as Brownian motion in a harmonic potential. This Gaussian Markov process has a bounded variance and admits a stationary probability distribution, in contrast to the standard Brownian motion. It…

We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…

This paper studies one-dimensional Ornstein-Uhlenbeck processes, with the distinguishing feature that they are reflected on a single boundary (put at level 0) or two boundaries (put at levels 0 and d>0). In the literature they are referred…

In this article, existence of the $k$-th order derivatives of local time $ \widehat{\alpha}^{(k)}(x,t)$ is considered for two d-dimensional fractional Ornstein-Uhlenbeck processes $X^{H_1}_t$ and $\widetilde{X}^{H_2}_s$ with Hurst…

We study absolute-continuity properties of a class of stochastic processes, including the gamma and the Dirichlet processes. We prove that the laws of a general class of non-linear transformations of such processes are locally equivalent to…

We are interested in the law of the first passage time of an Ornstein-Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first passage time of the process to members of a two-parameter…

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…

Let $X=(X_t)$ be a one-dimensional Ornstein-Uhlenbeck process with an initial density function $f$ supported on the positive real-line that is a regularly varying function with exponent $-(1+\eta)$, with $\eta\in (0,1)$. We prove the…

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…

For a dynamical system, it is known that the existence of a Lyapunov-type density function, called Lyapunov density or Rantzer's density function, implies convergence of Lebesgue almost all solutions to an equilibrium. Using the duality…

Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…

We prove that the first passage time density $\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\beta X dt + \sigma dW$ to reach a fixed threshold $\theta$ from a suprathreshold initial condition $x_0>\theta>0$ has a lower…