相关论文: On Lorden's Inequality and Renewal-Type Processes …

In queueing theory, Lorden's inequality can be used for bounds estimation of the moments of backward and forward renewal times. Two random variables called backwards renewal time and forward renewal time for this process are defined.…

It is more important to estimate the rate of convergence to a stationary distribution rather than only to prove the existence one in many applied problems of reliability and queuing theory. This can be done via standard methods, but only…

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…

We give a scheme of using the coupling method to obtain strong bounds for the convergence rate of the distribution of the backward renewal process in the total variation distance. This scheme can be applied to a wide class of regenerative…

Generalization of the Lorden's inequality is an excellent tool for obtaining strong upper bounds for the convergence rate for various complicated stochastic models. This paper demonstrates a method for obtaining such bounds for some…

We establish explicit exponential convergence estimates for the renewal theorem, in terms of a uniform component of the inter arrival distribution, of its Laplace transform which is assumed finite on a positive interval, and of the Laplace…

The main subject of the study in this paper is the simultaneous renewal time for two time-inhomogeneous Markov chains which start with arbitrary initial distributions. By a simultaneous renewal we mean the first time of joint hitting the…

We obtain a Lundberg-type inequality in the case of an inhomogeneous renewal risk model. We consider the model with independent, but not necessarily identically distributed, claim sizes and the interoccurrence times. In order to prove the…

We study the overshoot \(R_b=S_{\tau(b)}-b\) of a random walk with independent identically distributed increments from a standardised one-parameter exponential family, with primary emphasis on the small-drift regime \(\theta\downarrow0\).…

Let W be the number of points in (0,t] of a stationary finite-state Markov renewal point process. We derive a bound for the total variation distance between the distribution of W and a compound Poisson distribution. For any nonnegative…

We study a class of Markov processes that combine local dynamics, arising from a fixed Markov process, with regenerations arising at a state-dependent rate. We give conditions under which such processes possess a given target distribution…

We consider parameter estimation in a regression model corresponding to an iid sequence of censored observations of a finite state modulated renewal process. The model assumes a similar form as in Cox regression except that the baseline…

A class of discrete renewal processes with super-exponentially decaying inter-arrival distributions coincides with the infinite volume limit of general homogeneous pinning models in their localized phase. Pinning models are statistical…

The renewal contact process is a non-Markovian variant of the classical contact process in which recoveries are governed by independent renewal processes with interarrival distribution $\mu$. We establish new sufficient conditions ensuring…

We propose a constructive approach to building temporal point processes that incorporate dependence on their history. The dependence is modeled through the conditional density of the duration, i.e., the interval between successive event…

In this paper, we consider two time-inhomogeneous Markov chains $X^{(l)}_t$, $l\in\{1,2\}$, with discrete time on a general state space. We assume the existence of some renewal set $C$ and investigate the time of simultaneous renewal, that…

A famous result in renewal theory is the Central Limit Theorem for renewal processes. As in applications usually only observations from a finite time interval are available, a bound on the Kolmogorov distance to the normal distribution is…

Intermittency is a common and challenging problem in demand forecasting. We introduce a new, unified framework for building intermittent demand forecasting models, which incorporates and allows to generalize existing methods in several…

Restarting a deterministic process always impedes its completion. However, it is known that restarting a random process can also lead to an opposite outcome -- expediting completion. Hence, the effect of restart is contingent on the…

We study Markov processes conditioned so that their local time must grow slower than a prescribed function. Building upon recent work on Brownian motion with constrained local time in [5] and [33], we study transience and recurrence for a…