A Local Large Deviation Principle for Inhomogeneous Birth–Death Processes

Abstract

АннотацияThe paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled process contained within a neighborhood of a given continuous non-negative function.

A principle of large deviations for birth-death processes with a linear rate of downward jumps

“…Lemma 2.3. [1], [4] The distribution of the random process ξ( • ) on X T is absolutely continuous with respect to that of a process ζ( • ). The corresponding Radon-Nikodym density p = p T on X T has the form:…”

“…Earlier, the work [4] established an LLDP for the family of processes (1.3) when ϕ(T ) = T , while the paper [5] did it for the case where…”

On three methods for bounding the rate of convergence for some continuous-time Markov chains - invalid DOI

“…For details concerning possible applications of Markovian queues with time-dependent transitions we can refer to the work of Schwarz et al (2016), which contains a broad overview and a classification of time-dependent queueing systems considered up to 2016 and also the works of Crescenzo et al (2018), Giorno et al (2014), Granovsky and Zeifman (2004), Schwarz et al (2016), Zeifmann et al (20062014a), Vvedenskaya et al (2018), Olwal et al (2012), Wieczorek (2010), Li et al (2007), Almasi et al (2005), Moiseev and Nazarov (2016), Brugno et al (2017), Trejo et al (2019) and the references therein.…”

On the Three Methods for Bounding the Rate of Convergence for some Continuous-time Markov Chains

“…Then type (i) transitions describe Markovian queues with possibly state-dependent arrival and service intensities (for example, the classic M t (n)/M t (n)/1 queue); type (ii) transitions allow consideration of Markovian queues with state-independent batch arrivals and state-dependent service intensity; type (iii) transitions lead to Markovian queues with possible state-dependent arrival intensity and state-independent batch service; type (iv) transitions describe Markovian queues with state-independent batch arrivals and batch service. For the details concerning possible applications of Markovian queues with time-dependent transitions we can refer to [23], which contains a broad overview and a classification of time-dependent queueing systems considered up to 2016 and also [2,3,4,23,30,32,25,18,26,8,1,16] and references therein.…”