In this paper we consider two classes of reflected Ornstein–Uhlenbeck (OU) processes: the reflected OU process with jumps and the Markov-modulated reflected OU process. We prove that their stationary distributions exist. Furthermore, for the jump reflected OU process, the Laplace transform (LT) of the stationary distribution is given. As for the Markov-modulated reflected OU process, we derive ...

Stationary-phase cells displayed a distribution of relaxed plasmids and had the ability to recover plasmid supercoiling as soon as nutrients became available. Preexisting gyrase molecules in these cells were responsible for this recovery. Stationary-phase rpoS cells showed a bimodal distribution of plasmids and failed to supercoil plasmids after the addition of nutrients, suggesting that rpoS p...

In this work, we prove the existence and uniqueness of a quasi-stationary distribution for hypoelliptic Hamiltonian dynamics system N particles in $${\mathbb {R}}^d$$ interacting with Lennard-Jones type potentials or repulsive Coulomb potentials.

Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of weights for a given time horizon T . However, in many scenarios, the time horizon is not fixed, but the stopping time is chosen according to some distribution...

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively diierent regimes are observed, corresponding to intermittent and regular behaviour. In the boundary between them, the mean value of the relevant variable is...

We study a stochastic multiplicative process with reset events. It is shown that the model develops a stationary power-law probability distribution for the relevant variable, whose exponent depends on the model parameters. Two qualitatively different regimes are observed, corresponding to intermittent and regular behavior. In the boundary between them, the mean value of the relevant variable is...

In this paper, we propose a method of analyzing time series, called the spatial analysis. The analysis consists mainly of the statistical inference on the distribution given by the expected local time, which we define to be the spatial distribution, of a given time series. The spatial distribution is introduced primarily for the analysis of nonstationary time series whose distributions change o...