Related papers: Statistical inference for generalized Ornstein-Uhl…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
In this paper we study the L\'evy Ornstein- Uhlenbeck equation $\partial_t X_t=-m\,X_t+\eta$. The transition kernel of the L\'evy Ornstein- Uhlenbeck process is given by a series which is not convergent in general, a large diffusion…
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 investigate ergodic properties of generalized Ornstein--Uhlenbeck processes. In particular, we provide sufficient conditions for ergodicity, and for subexponential and exponential convergence to the invariant probability measure. We use…
This paper is devoted to parameter estimation of the mixed fractional Ornstein-Uhlenbeck process with a drift. Large sample asymptotical properties of the Maximum Likelihood Estimator is deduced using the Laplace transform computations or…
Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator of…
This article establishes cutoff thermalization (also known as the cutoff phenomenon) for a class of generalized Ornstein-Uhlenbeck systems $(X^\varepsilon_t(x))_{t\geqslant 0}$ with $\varepsilon$-small additive L\'evy noise and initial…
We consider nonparametric statistical inference for L\'evy processes sampled irregularly, at low frequency. The estimation of the jump dynamics as well as the estimation of the distributional density are investigated. Non-asymptotic risk…
Via a Bismut-Elworthy-Li formula from [KPP23], we derive uniform gradient estimates for transition semigroups associated with stochastic differential equations driven by a large class of cylindrical L\'{e}vy processes which includes the…
L\'evy processes, known for their ability to model complex dynamics with skewness, heavy tails and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most L\'evy processes, whether in…
We study sparsity-regularized maximum likelihood estimation for the drift parameter of high-dimensional non-stationary Ornstein--Uhlenbeck processes given repeated measurements of i.i.d. paths. In particular, we show that Lasso and Slope…
We consider the generalized Ornstein- Uhlenbeck equation $\partial_t X=-m X_t+\eta$. In this paper We construct the L\'evy noise $\eta$. The generalized Ornstein- Uhlenbeck process $X_t$ will be represented by a special types of graphs…
Stochastic differential equations such as the Ornstein-Uhlenbeck process have long been used to model realworld probablistic events such as stock prices and temperature fluctuations. While statistical methods such as Maximum Likelihood…
We present a time change construction of affine processes with state-space $\mathbb{R}_+^m\times \mathbb{R}^n$. These processes were systematically studied in (Duffie, Filipovi\'c and Schachermayer, 2003) since they contain interesting…
We construct a generalization of the Ornstein-Uhlenbeck processes on the cone of covariance matrices endowed with the Log-Euclidean and the Affine-Invariant metrics. Our development exploits the Riemannian geometric structure of symmetric…
We consider the Ornstein-Uhlenbeck process with a broad initial probability distribution (Levy distribution), which exhibits so-called non-spectral modes. The relaxation of such modes differs from those determined from the parameters of the…
We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt…
Moving average processes driven by exponential-tailed L\'evy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps.…
We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…
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…