Related papers: A set-indexed Ornstein-Uhlenbeck process
Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…
We study the first-passage dynamics of a non-Markovian stochastic process with time-averaged feedback, which we model as a one-dimensional Ornstein--Uhlenbeck process wherein the particle drift is modified by the empirical mean of its…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
We study the positive recurrence of piecewise Ornstein-Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two…
Empirical studies indicate the existence of long range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein--Uhlenbeck…
The $q$-Ornstein-Uhlenbeck processes, $q\in(-1,1)$, are a family of stationary Markov processes that converge weakly to the standard Ornstein-Uhlenbeck process as $q$ tends to 1. It has been noticed recently that in terms of path…
Even in a simple stochastic process, the study of the full distribution of time integrated observables can be a difficult task. This is the case of a much-studied process such as the Ornstein-Uhlenbeck process where, recently, anomalous…
We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of $p$-tempered $\alpha$-stable ($\ts$) distributions. Our results hold for both the univariate and multivariate cases and we consider…
We introduce a class of L\'evy-driven graph Ornstein-Uhlenbeck (grOU) models for edge-indexed network time series. The proposed framework extends generalized network autoregressive (GNAR) processes for edge-indexed network time series to…
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…
Consider a set of continuous maps from the interval $[0,1]$ to a domain in ${\mathbb R}^d$. Although the topological boundary of this set in the path space is not smooth in general, by using the theory of functions of bounded variation (BV…
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 paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein-Uhlenbeck process which is defined as the solution of $dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t$, and which is observed in…
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 introduce a notion of intervention for stochastic differential equations and a corresponding causal interpretation. For the case of the Ornstein-Uhlenbeck SDE, we show that the SDE resulting from a simple type of intervention again is an…
In this paper, we consider an ergodic Ornstein-Uhlenbeck process with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its jump intensity depend on unknown parameters.…
Stochastic oscillators play a prominent role in different fields of science. Their simplified description in terms of a phase has been advocated by different authors using distinct phase definitions in the stochastic case. One notion of…
The survival probability for a periodic non-autonomous Ornstein-Uhlenbeck process is calculated analytically using two different methods. The first uses an asymptotic approach. We treat the associated Kolmogorov Backward Equation with an…
The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of…
Orey suggested the definition of some index for Gaussian processes with stationary increments which determines various properties of the sample paths of this process. We give an extension of the definition of the Orey index for a second…