We introduce the concept of asymptotic period for an irreducible and aperiodic discrete-time Markov chain on a countable state space. If the chain is transient its asymptotic period may be larger than one. We present some sufficient conditions and, in the more restricted setting of birth-death processes, a necessary and sufficient condition for asymptotic aperiodicity . It is subsequently shown...

For birth and death processes with finite state space, we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are again birth and death processes when the right boundary point is absorbing. On the other hand, it ...

Let Tn be the compact convex set of tridiagonal doubly stochastic matrices. These arise naturally in probability problems as birth and death chains with a uniform stationary distribution. We study ‘typical’ matrices T ∈ Tn chosen uniformly at random in the set Tn. A simple algorithm is presented to allow direct sampling from the uniform distribution on Tn. Using this algorithm, the elements abo...

OBJECTIVE To describe the progression of human immunodeficiency virus (HIV) disease through clinical stages from birth to death among a large number of perinatally infected children. METHODS The Pediatric Spectrum of Disease (PSD) project, coordinated by the Centers for Disease Control and Prevention (CDC), has conducted active surveillance for HIV disease since 1988 in seven geographic regio...

BACKGROUND The average age of women bearing their first child has increased strongly. This is an important reproductive health problem as fertility declines with increasing female age. Unfortunately, IVF using fresh oocytes cannot compensate for this age-related fertility decline. Oocyte freezing could be a solution. METHODS We used the Markov model to estimate the cost-effectiveness of three...

The paper deals with the performance optimization for skim milk powder unit of a dairy plant at National Dairy Research Institute (N. D. R. I.), Karnal using Genetic Algorithm (G. A.). The skim milk powder unit comprises of six subsystems working in series. The failure and repair rates of the subsystems are taken from maintenance history sheets, which follow the exponential distribution. The ma...

For continuous-time Markov chains, we provide criteria for non-ergodicity, non-algebraic ergodicity, non-exponential and non-strong ergodicity. discrete-time ergodicity are given. Our in terms of the existence solutions to inequalities involving Q-matrix (or transition matrix P time-discrete case) chain. Meanwhile, these practical applied some examples, including a special class single birth pr...

the notion of infinite order markov process is introduced and the markov property of the flow of information is established.