Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on system size (corresponding to number of products or customers undergoing birth-death process) thus vary every time occurs, which makes fluctuations in inevitable. The differential-difference equation governing evolution such a process is well established, but it resists solving for...

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computation...

In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We d...

Continued fractions (CFs) play a fundamental role in many investigations due to its applications to diverse fields like number theory, special functions, approximations, moment problems, digital networks, statistics, and signal processing. Their importance has grown further with the advent of fast computing facilities. The problem of converting a continued fraction into a power series is import...

When modeling longitudinal data using a set of hidden processes such as state-space models, a common assumption is that the number of hidden processes is fixed, and all hidden processes have the same life span (i.e., all start at the onset of the data stream and terminate at the end of the data stream). In this report I outline a framework of modeling complex longitudinal data using a birth-dea...

Fault tolerance by redundancy is a key technique for improving web services reliability. But, the reliability and fault tolerance are not well supported by Service-oriented architecture (SOA) conceptual model.Most of the existing analytical models to predict the reliability of web services assume their structures are static which do not conform to reality and the estimated reliability precision...

We develop the Dynamic Chinese Restaurant Process (DCRP) which incorporates time-evolutionary feature in dependent Dirichlet Process mixture models. This model can capture the dynamic change of mixture components, allowing clusters to emerge, vanish and vary over time. All these macroscopic changes are controlled by tracing the birth and death of every single element. We investigate the propert...