Related papers: Asymptotics of the occupancy scheme in a random en…
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distributed (iid), we assume that they follow a regime switching…
In the classical occupancy scheme, one considers a fixed discrete probability measure ${\bf p}=(p_i: {i\in{\cal I}})$ and throws balls independently at random in boxes labeled by ${\cal I}$, such that $p_i$ is the probability that a given…
The paper studies asymptotic behavior of the loss probability for the $GI/M/m/n$ queueing system as $n$ increases to infinity. The approach of the paper is based on applications of classic results of Tak\'acs (1967) and the Tauberian…
This paper collects facts about the number of occupied boxes in the classical balls-in-boxes occupancy scheme with infinitely many positive frequencies: equivalently, about the number of species represented in samples from populations with…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
For a Markov chain $Y$ with values in a Polish space, consider the entrance chain, obtained by sampling $Y$ at the moments when it enters a fixed set $A$ from its complement $A^c$. Similarly, consider the exit chain, obtained by sampling…
In this paper, we analyze the number of departures from an initially empty $M/M/\infty$ system in a finite time interval. We observe the system during an exponentially distributed period of time starting from the time origin. We then…
We study the asymptotic behavior of a Markov chain on $\mathbb{Z}^2$ that corresponds to the two-dimensional marginals of a reinforcement process on $\mathbb{Z}^{\mathbb{N}}$. Three distinct asymptotic regimes are identified, depending on…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
In this work, we consider an inhomogeneous (discrete time) Markov chain and are interested in its long time behavior. We provide sufficient conditions to ensure that some of its asymptotic properties can be related to the ones of a…
Let $X_1,X_2,...$ be a sequence of random variables satisfying the distributional recursion $X_1=0$ and $X_n= X_{n-I_n}+1$ for $n=2,3,...$, where $I_n$ is a random variable with values in $\{1,...,n-1\}$ which is independent of…
We study the asymptotics of the $p$-mapping model of random mappings on $[n]$ as $n$ gets large, under a large class of asymptotic regimes for the underlying distribution $p$. We encode these random mappings in random walks which are shown…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
We consider general transformations of random walks on groups determined by Markov stopping times and prove that the asymptotic entropy (resp., rate of escape) of the transformed random walks is equal to the asymptotic entropy (resp., rate…
A semi-Markov process is one that changes states in accordance with a Markov chain but takes a random amount of time between changes. We consider the generalisation to semi-Markov processes of the classical Lamperti law for the occupation…
We describe a Markov-Chain-Monte-Carlo algorithm which can be used to generate naturally labeled n-element posets at random with a probability distribution of one's choice. Implementing this algorithm for the uniform distribution, we…
This paper provides the asymptotic analysis of the loss probability in the $GI/M/1/n$ queueing system as $n$ increases to infinity. The approach of this paper is alternative to that of the recent papers of Choi and Kim [2000] and Choi et al…
The paper concerns the classical occupancy scheme with infinitely many boxes. We establish approximations to the distributions of the number of occupied boxes, and of the number of boxes containing exactly r balls, within the family of…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…