# Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes

@inproceedings{Abramov2022ConditionsFR, title={Conditions for recurrence and transience for time-inhomogeneous birth-and-death processes}, author={Vyacheslav M. Abramov}, year={2022} }

We derive the conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results by Menshikov and Volkov [Electron. J. Probab., 13 (2008), paper No. 31, 944--960] follow.

## References

SHOWING 1-10 OF 16 REFERENCES

### Urn-related random walk with drift x /

- Mathematics
- 2008

We study a one-dimensional random walk whose expected drift depends both on time and the position of a particle. We establish a non-trivial phase transition for the recurrence vs. transience of the…

### Necessary and sufficient conditions for the convergence of positive series

- MathematicsJournal of Classical Analysis
- 2022

We provide new necessary and sufficient conditions for the convergence of positive series developing Bertran–De Morgan and Cauchy type tests given in [M. Martin, Bull. Amer. Math. Soc. 47(1941),…

### Limit Theorems for Stochastic Processes

- Mathematics
- 1987

I. The General Theory of Stochastic Processes, Semimartingales and Stochastic Integrals.- II. Characteristics of Semimartingales and Processes with Independent Increments.- III. Martingale Problems…

### Theory of Martingales

- Mathematics
- 2013

In this article, we discuss some advanced results in the theory of martingales and their application in operations research and management science. These results include (i) martingale inequalities,…

### Conservative and Semiconservative Random Walks: Recurrence and Transience

- Mathematics
- 2016

In the present paper, we define conservative and semiconservative random walks in $$\mathbb {Z}^d$$Zd and study various families of random walks. The family of symmetric random walks is one of the…

### Limit non-stationary behavior of large closed queueing networks with bottlenecks

- Mathematics, Computer ScienceQueueing Syst. Theory Appl.
- 1993

In this paper martingales methods are applied for analyzing limit non-stationary behavior of the queue length processes in closed Jackson queueing networks with a single class consisting of a large…

### Extension of the Bertrand–De Morgan Test and Its Application

- MathematicsAm. Math. Mon.
- 2020

A simple proof for the extended Bertrand–De Morgan test is provided and an application of that test to the theory of birth-and-death processes is demonstrated.

### State-Dependent Benes Buffer Model with Fast Loading and Output Rates

- Computer Science
- 1995

A state-dependent generalization of the exponential Benes model of single-source buffer system in which the source process consists of alternating transmission and idle periods is considered, which shows that in heavy traffic the buffer content grows linearly in N, while the deviations of the order √ N from the deterministic limit are approximated by the Gaussian diffusion process.

### A large closed queueing network with autonomous service and bottleneck

- MathematicsQueueing Syst. Theory Appl.
- 2000

This paper studies the queue-length process in a closed Jackson-type queueing network with the large number N of homogeneous customers by methods of the theory of martingales and by the up- and…

### Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution

- MathematicsAnn. Oper. Res.
- 2006

The paper establishes the stability condition and studies a behavior of the limiting queue-length distributions as μ2 increases to infinity, and proves the convergence of appropriate queue- length distributions to those of the associated “usual” multiserver queueing system without retrials.