This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process.

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process.

background & aim: congenital hypothyroidism (ch) is one of the most common endocrine diseases and is a major cause of preventable mental retardation. early diagnosis of ch can help prevent future diseases. although time series techniques are often utilized to forecast future status, they are inadequate to deal with count data with overdispersion. the aim of this study was to apply poisson hidde...

Models for spatial point processes are characterized as the stationary distributions of spatial birth and death processes. The Markov chain Monte Carlo algorithm determined by the underlying birth and death process immediately gives a method of simulation, and the time-invariance method of estimation proposed by Baddeley (2000) gives a general method for deriving parameter estimates for the mod...

Lattice birth-and-death Markov dynamics of particle systems with spins from Z+ are constructed as unique solutions to certain stochastic equations. Pathwise uniqueness, strong existence, Markov property and joint uniqueness in law are proven, and a martingale characterization of the process is given. Sufficient conditions for the existence of an invariant distribution are formulated in terms of...

We study the uniform convergence to quasi-stationarity of multidimensional processes absorbed when one coordinates vanishes. Our results cover competitive or weakly cooperative Lotka–Volterra birth and death Feller diffusions with interaction. To this aim, we develop an original non-linear Lyapunov criterion involving two functions, which applies general Markov processes.

A competition process is a continuous time Markov chain that can be interpreted as system of interacting birth-and-death processes, the components which evolve subject to competitive interaction. This paper devoted study long-term behaviour such process, where component increases with linear birth rate and decreases given by function other components. zero an absorbing state for each component,...

A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretic...