相关论文: Ornstein-Uhlenbeck-Cauchy Process
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…
The Ornstein-Uhlenbeck process can be seen as a paradigm of a finite-variance and statistically stationary rough random walk. Furthermore, it is defined as the unique solution of a Markovian stochastic dynamics and shares the same local…
We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by L\'{e}vy processes. The emphasis is on the different contexts in which these processes arise, such as stochastic partial differential…
In this article we prove new results regarding the existence of Bernstein processes associated with the Cauchy problem of certain forward-backward systems of decoupled linear deterministic parabolic equations defined in Euclidean space of…
We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein-Uhlenbeck process with Levy noise and bounded drift. We…
Markovian diffusion processes yield a system of conservation laws which couple various conditional expectation values (local moments). Solutions of that closed system of deterministic partial differential equations stand for a regular…
The small noise cut-off phenomenon in continuous time and space has been studied in the recent literature for the linear and non-linear stable Langevin dynamics with additive L\'evy drivers - understood as abrupt thermalization of the…
In this paper we introduce the well-balanced L\'{e}vy driven Ornstein-Uhlenbeck process as a moving average process of the form $X_t=\int \exp(-\lambda |t-u|)dL_u$. In contrast to L\'{e}vy driven Ornstein-Uhlenbeck processes the…
We consider the problem of estimation of the drift parameter of an ergodic Ornstein--Uhlenbeck type process driven by a L\'evy process with heavy tails. The process is observed continuously on a long time interval $[0,T]$, $T\to\infty$. We…
Distributional properties -including Laplace transforms- of integrals of Markov processes received a lot of attention in the literature. In this paper, we complete existing results in several ways. First, we provide the analytical solution…
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…
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process…
We study the Cauchy problem involving non-local Ornstein-Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the L\'evy measure corresponding to the large jumps part has a first…
We consider equations of nonlinear transport on the circle with regular self interactions appearing in aggregation models and deterministic mean field dynamics. We introduce a random perturbation of such systems through a stochastic…
In this work, we study the class of stochastic process that generalizes the Ornstein-Uhlenbeck processes, hereafter called by \emph{Generalized Ornstein-Uhlenbeck Type Process} and denoted by GOU type process. We consider them driven by the…
We study the stationary fluctuations of independent run-and-tumble particles. We prove that the joint densities of particles with given internal state converges to an infinite dimensional Ornstein-Uhlenbeck process. We also consider an…
In this article we introduce a theory of integration for deterministic, operator-valued integrands with respect to cylindrical L\'evy processes in separable Banach spaces. Here, a cylindrical L\'evy process is understood in the classical…
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…
The Ornstein-Uhlenbeck (OU) process describes the dynamics of Brownian particles in a confining harmonic potential, thereby constituting the paradigmatic model of overdamped, mean-reverting Langevin dynamics. Despite its widespread…
We study high-dimensional drift estimation for L\'evy-driven Ornstein--Uhlenbeck processes based on discrete observations. Assuming sparsity of the drift matrix, we analyze Lasso and Slope estimators constructed from approximate likelihoods…