Methods using regeneration have been used to draw approximations to the stationary distribution of Markov Chain Monte Carlo processes. We introduce an algorithm that allows exact sampling of the stationary distribution through the use of a regeneration method and a Bernoulli Factory to select samples within each regeneration cycle that are shown to be from the desired density. We demonstrate th...

We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many interesting implications, including an illustration of the Archimedes’ principle. The analysis rests on constructing reflecting Brownian motion with drift in a genera...

We study the stability of single server retrial queues under general distribution for retrial times and stationary ergodic service times, for three main retrial policies studied in the literature: classical linear, constant and control policies. The approach used is the renovating events approach to obtain sufficient stability conditions by strong coupling convergence of the process modeling th...

In this paper we study some properties related to the distribution of membership grades for non-stationary fuzzy sets. We obtain the formulation for the distribution, where the non-stationary fuzzy sets are obtained by generating instantiations about the center values. The two cases considered are for the underlying membership functions as Triangular and Gaussian. The analytical results obtaine...

This paper discusses the stochastic nuclear spin generator systems under the influence of white noise. We prove the existence of a unique solution and a stationary distribution for stochastic nuclear spin generator systems. We analyze long-time behaviour of random attractor of the distributions of the solutions. Furthermore, we prove that the random attractor contains of only one point for part...

We investigate how the stationary distribution of a Markov chain changes when transitions from a single state are modified. In particular, adding a single directed edge to nearest neighbor random walk on a finite discrete torus in dimensions one, two, or three changes the stationary distribution linearly, logarithmically, or only locally. Related results are derived for birth and death chains a...

The Grassmann, Taksar, and Heyman (GTH) algorithm for the computation of the stationary distribution of a finite stochastic matrix is shown to apply for the general case when there is a unique stationary distribution. The approach is elementary and matrix based, with probabilistic arguments avoided, to give insight into the essential structural properties. A byproduct is a necessary and suffici...

We consider the following random process on the complete graph: repeatedly draw edges (with replacement) and with probability p assign the vertices of the edge blue and with probability 1 − p assign the vertices of the edge red. This is a random walk on a state space of red/blue colorings of the complete graph and so has a stationary distribution. We derive this stationary distribution as well ...

In this paper we generalize existing results for the steady-state distribution of growthcollapse processes with independent exponential intercollapse times to the case where they have a general distribution on the positive real line having a finite mean. In order to compute the moments of the stationary distribution, no further assumptions are needed. However, in order to compute the stationary...

This paper reports on work aimed at extending stable population theory to include immigration. its central findings is that, as long as fertility is below replacement, a constant number and age distribution of immigrants (with fixed fertility and mortality schedules) lead to a stationary population. Neither the level of the net reproduction rate nor the size of the annual immigration affects th...