Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an apparent stochastic equilibrium for long periods. These distributions have some drawbacks: they need not exist, nor be unique, and their calculation can present p...

Consider a single server queue in which the service station may breakdown according to a Poisson process with rates γ in busy time and γ’ in idle time respectively. After a breakdown, the service station will be repaired immediately and the repair time is assumed to have an exponential distribution with rate δ. Suppose the arrival time has an exponential distribution with rate λ, and the probab...

Abstract Ecologists and fisheries scientists are faced with forecasting the ecological responses of non-stationary processes resulting from climate change other drivers. While much is known about temporal change, vis-à-vis species distributional shifts, less how spatial variability in population structure changes through time response to trends A experiencing decreasing would be expected more e...

We consider a one-dimensional stationary stochastic process $x(\tau)$ of duration $T$. study the probability density function (PDF) $P(t_{\rm m}|T)$ time $t_{\rm m}$ at which reaches its global maximum. By using path integral method, we compute for number equilibrium and nonequilibrium processes, including Ornstein-Uhlenbeck process, Brownian motion with resetting single confined run-and-tumble...

The evolutionary algorithm stochastic process is well-known to be Markovian. These have been under investigation in much of the theoretical evolutionary computing research. When mutation rate is positive, the Markov chain modeling an evolutionary algorithm is irreducible and, therefore, has a unique stationary distribution, yet, rather little is known about the stationary distribution. In fact,...

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco [4] studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Φ on the space of probability distributions on {1, 2, . . .}. In the case of a birth-death process, one ca...

In this paper we study a storage process or a liquid queue in which the input process is the local time of a positively recurrent stationary diffusion in stationary state and the potential output takes place with a constant deterministic rate. For this storage process we find its stationary distribution and compute the joint distribution of the starting and ending times of the busy and idle per...

In this paper, we introduce a storage process with singular continuous input and random output. That is the input process is defined by the local time at zero of a stationary reflecting Brownian motion with drift, and the output process is a strictly-stable subordinator. We show that the storage process is stationary in stationary state, and using some characters of subordinators, we derive the...