Related papers: Ratio limit theorem for renewal processes
Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977)…
The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…
We consider a run-and-tumble particle (RTP) with stochastic resetting confined to the half line $[0,\infty)$ with a sticky boundary at $x=0$. In the bulk the RTP tumbles at a constant rate $\alpha>0$ between velocity states $\pm v$ with…
We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at $0$ whenever they cross that point. We show that the perturbed random walk, after being…
We consider one dimensional random walks in random environment where every time the process stays at a location, it dies with a fixed probability. Under some mild assumptions it is easy to show that the survival probability goes to zero as…
We consider renewal-type processes whose positive inter-renewal times may be dependent, non-identically distributed, and may have mixed distributions. We introduce a generalised intensity measure extending the classical hazard-rate…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
Reaction-diffusion process with exclusion in the presence of traps has been studied. The asymptotic survival probability for the case of uniformly distributed random traps shows a stretched e\ xponential behavior. We show that additional…
This article is devoted to the investigation of limit theorems for mixed max-sum processes with renewal type stopping indexes. Limit theorems of weak convergence type are obtained as well as functional limit theorems.
This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process…
Let {X_n,n\geq0} be a Markov chain on a general state space X with transition probability P and stationary probability \pi. Suppose an additive component S_n takes values in the real line R and is adjoined to the chain such that…
The ability to estimate the rate of convergence for the distributions of regenerative processes is in great demand. These processes are often encountered in queuing theory and in related problems. In some papers on regenerative processes,…
We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…
Consider a system consisting of multiple sockets into each of which a component is inserted. If a component fails, it is replaced immediately and system operation resumes. Then the failure process of the system is the superposition of…
We analyze the dynamics of random walks with long-term memory (binary chains with long-range correlations) in the presence of an absorbing boundary. An analytically solvable model is presented, in which a dynamical phase-transition occurs…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
In this paper we consider two branching processes living in a joint random environment. Assuming that both processes are critical we address the following question: What is the probability that both populations survive up to a large time…
We analyse the ruin probabilities for a renewal insurance risk process with inter-arrival time distributions depending on the claims that arrived within a fixed (past) time window. This dependence could be explained through a regenerative…
A sufficient condition is obtained for a discrete-time birth-death process to possess the strong ratio limit property, directly in terms of the one-step transition probabilities of the process. The condition encompasses all previously known…