Related papers: Regenerative processes
We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the…
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be…
Scaled type Markov renewal processes generalize classical renewal processes: renewal times come from a one parameter family of probability laws and the sequence of the parameters is the trajectory of an ergodic Markov chain. Our primary…
The work continues the author's many-year research in theory of maximal branching processes, which are obtained from classical branching processes by replacing the summation of descendant numbers with taking the maximum. One can say that in…
The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…
We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit…
We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and…
Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the…
Some characterizations of mixed renewal processes in terms of exchangeability and of different types of disintegrations are given. As a consequence, an existence result for mixed renewal processes, providing also a new construction for…
We consider random processes that are history-dependent, in the sense that the distribution of the next step of the process at any time depends upon the entire past history of the process. In general, therefore, the Markov property cannot…
In stochastic models for queues and their networks, random events evolve in time. A process for their backward evolution is referred to as a time reversed process. It is often greatly helpful to view a stochastic model from two different…
We consider stochastic processes indexed by the vertices of an infinite binary tree having a simple recursive structure. The value at any vertex is some fixed function of the values at the two daughter vertices together with some…
This paper concerns the recurrence structure of the infinite server queue, as viewed through the prism of the maximum dater sequence, namely the time to drain the current work in the system as seen at arrival epochs. Despite the importance…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
The role of geometrically infinitely divisible laws in renewal equations and superposition of renewal processes are explored here. Some examples are also discussed.
We study the generalization of the G/G/1 queue obtained by relaxing the assumption of independence between inter-arrival times and service requirements. The analysis is carried out for the class of multivariate matrix exponential…
Given a sequence of i.i.d. random functions $\Psi_{n}:\mathbb{R}\to\mathbb{R}$, $n\in\mathbb{N}$, we consider the iterated function system and Markov chain which is recursively defined by $X_{0}^{x}:=x$ and…
In the last decade Hawkes processes have received much attention as models for functional connectivity in neural spiking networks and other dynamical systems with a cascade behavior. In this paper we establish a renewal approach for…
We consider a single server retrial queue with the server subject to interruptions and classical retrial policy for the access from the orbit to the server. We analyze the equilibrium distribution of the system and obtain the generating…
Motivated by queueing applications, we study various reflected autoregressive processes with dependencies. Amongst others, we study cases where the interarrival and service times are proportionally dependent with additive and/or subtracting…