Related papers: Time-changed fractional Ornstein-Uhlenbeck process

Time-changed stochastic processes have attracted great attention and wide interests due to their extensive applications, especially in financial time series, biology and physics. This paper pays attention to a special stochastic process,…

This paper consider the LAN property for the mixed O-U process under high-frequency observation when H>3/4. As considered in mixed fractional Brownian motion, we will also use the projection step to get the non-diagonal rate matrix.

Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…

Several important properties of positive semidefinite processes of Ornstein--Uhlenbeck type are analysed. It is shown that linear operators of the form $X\mapsto AX+XA^{\mathrm{T}}$ with $A\in M_d(\mathbb{R})$ are the only ones that can be…

Partially observed stochastic systems can appear (almost) time-reversal symmetric while in fact operating far from equilibrium. The present work extends the perturbative framework introduced in [Phys. Rev. Lett. 136, 198302 (2026)] to…

We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an…

In this paper we consider an Ornstein-Uhlenbeck (OU) process $(M(t))_{t\geqslant 0}$ whose parameters are determined by an external Markov process $(X(t))_{t\geqslant 0}$ on a finite state space $\{1,\ldots,d\}$; this process is usually…

We investigate large deviation properties of the maximum likelihood drift parameter estimator for Ornstein--Uhlenbeck process driven by mixed fractional Brownian motion.

In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…

We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…

We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge…

Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

We study the statistical properties of first-passage Brownian functionals (FPBFs) of an Ornstein-Uhlenbeck (OU) process in the presence of stochastic resetting. We consider a one dimensional set-up where the diffusing particle sets off from…

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to…

We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…

Let $\mathcal P_2$ be the space of probability measures on $\R^d$ having finite second moment, and consider the Riemannian structure on $\mathcal P_2$ induced by the intrinsic derivative on the $L^2$-tangent space. By using stochastic…

This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics during random time…

The multivariate Ornstein-Uhlenbeck process is used in many branches of science and engineering to describe the regression of a system to its stationary mean. Here we present an $O(N)$ Bayesian method to estimate the drift and diffusion…

We provide necessary and sufficient conditions for a Hilbert space-valued Ornstein-Uhlenbeck process to be reversible with respect to its invariant measure $\mu$. For a reversible process the domain of its generator in $L^p(\mu )$ is…