Abstract In this paper, we propose a new type of univariate and bivariate Integer-valued autoregressive model order one (INAR(1)) to approximate linear birth death process with constant rates. Under specific parametric setting, the dynamic transition probabilities probability generating function INAR(1) will converge that as length subintervals goes 0. Due simplicity Markov structure, maximum l...

Classic works of Karlin-McGregor and Jones-Magnus have established a general correspondence between continuous-time birth-and-death processes and continued fractions of the Stieltjes-Jacobi type together with their associated orthogonal polynomials. This fundamental correspondence is revisited here in the light of the basic relation between weighted lattice paths and continued fractions otherwi...

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with n current particles, a new particle is born with instantaneous rate λ(n) and a particle dies with instantaneous rate μ(n). Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death proce...

The birth and death processes are closely related to the orthogonal polynomials. The latter allows determining the stochastic matrix associated with these processes. Let us also note that these processes are stationary Markov processes whose state space is the nonnegative integers. Many authors treated the question of the existing relationship between the birth and death processes and the ortho...

Standard proofs of the ergodic theorems of demography rely on theorems borrowed from positive matrix theory, tauberian theory, and the theory of time-inhomogeneous Markov matrices. These proofs are efficient and expedient, but they give little direct insight into the mechanism that causes ergodicity. This paper proposes a simple and unified proof of the two ergodic theorems. It is shown that th...

this paper discusses the performance evaluation and availability analysis of ammonia synthesis unit of a fertilizer plant. the fertilizer plant is a complex and repairable engineering system comprises of various units viz. shell gasification and carbon recovery, desulphurization, co-shift conversion, decarbonation, nitrogen wash and ammonia synthesis etc. one of the most important functionaries...

the present paper deals with development of a simulation model for the performance evaluation of feed water system of a thermal power plant using markov birth-death process and probabilistic approach. in present paper, the feed water system consists of four subsystems. after drawing transition diagram for feed water system, differential equations are developed and then solved recursively using ...