Related papers: Multivariate supOU processes
Using a coupling for the weighted sum of independent random variables and the explicit expression of the transition semigroup of Ornstein-Uhlenbeck processes driven by compound Poisson processes, we establish the existence of a successful…
This paper deals with the realisation of affine constraints on nonreversible stochastic differential equations (SDE) by strong confining forces. We prove that the confined dynamics converges pathwise and on bounded time intervals to the…
Active Ornstein-Uhlenbeck particles (AOUPs) are overdamped particles in an interaction potential subject to external Ornstein-Uhlenbeck noises. They can be transformed into a system of underdamped particles under additional velocity…
Exponential functionals of L\'evy processes appear as stationary distributions of generalized Ornstein-Uhlenbeck (GOU) processes. In this paper we obtain the infinitesimal generator of the GOU process and show that it is a Feller process.…
Consider a multivariate L\'evy-driven Ornstein-Uhlenbeck process where the stationary distribution or background driving L\'evy process is from a parametric family. We derive the likelihood function assuming that the innovation term is…
We study the aggregation of AR processes and generalized Ornstein-Uhlenbeck (OU) processes. Mixture of spectral densities with random poles are the main tool. In this context, we apply our results for the aggregation of doubly stochastic…
Starting from the notion of multivariate fractional Brownian Motion introduced in [F. Lavancier, A. Philippe, and D. Surgailis. Covariance function of vector self-similar processes. Statistics & Probability Letters, 2009] we define a…
We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and…
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…
Consider the linear stochastic differential equation (SDE) on $\mathbb{R}^n$: \[\mathrm {d}{X}_t=AX_t\,\mathrm{d}t+B\,\mathrm{d}L_t,\] where $A$ is a real $n\times n$ matrix, $B$ is a real $n\times d$ real matrix and $L_t$ is a L\'{e}vy…
Active matter systems are driven out of equilibrium by conversion of energy into directed motion locally on the level of the individual constituents. In the spirit of a minimal description, active matter is often modeled by so-called active…
We establish sufficient conditions for the existence, and derive explicit formulas for the $\kappa$'th moments, $\kappa \geq 1$, of Markov modulated generalized Ornstein-Uhlenbeck processes as well as their stationary distributions. In…
The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time…
This paper presents an identity between the multivariate and univariate saddlepoint approximations applied to sample path probabilities for a certain class of stochastic processes. This class, which we term the recursively compounded…
In this paper, we study Ornstein-Uhlenbeck processes with Markov modulation, whose parameters depend on an external underlying two-state Markov process. Conditional mean and variance of such processes under given modulation are investigated…
Spatio-temporal modelling is an increasingly popular topic in Statistics. Our paper contributes to this line of research by developing the theory, simulation and inference for a spatio-temporal Ornstein-Uhlenbeck process. We conduct…
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major…
Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to L\'evy-driven…
It has been recently discovered that some random processes may satisfy limit theorems even though they exhibit intermittency, namely an unusual growth of moments. In this paper we provide a deeper understanding of these intricate limiting…
The Ornstein--Uhlenbeck Particle (OUP) model imagines a microscopic swimmer propelled by an active force which is correlated with itself on a finite time-scale. Here we investigate the influence of external potentials on an ideal suspension…