• Corpus ID: 254247120

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

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



Urn-related random walk with drift x /

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

  • V. Abramov
  • Mathematics
    Journal 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

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

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

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

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

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

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

  • V. Abramov
  • Mathematics
    Queueing 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

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.