This paper studies the f-ergodicity and its exponential convergence rate for continuous-time Markov chain. Assume f is square integrable, reversible chain, it proved that of holds if only spectral gap generator positive. Moreover, equal to gap. For irreversible case, positivity remains a sufficient condition f-ergodicity. The effectiveness these results are illustrated by some typical examples.

Planning for supply water demands (drinkable and irrigation water demands) is a necessary problem. For this purpose, three subjects must be considered (optimization of water supply systems such as volume of reservoir dams, optimization of released water from reservoir and prediction of next droughts). For optimization of volume of reservoir dams, yield model is applied. Reliability of yield mod...

We study new formulas based on Lyapunov exponents for entropy, mutual information, and capacity of finite state discrete time Markov channels. We also develop a method for directly computing mutual information and entropy using continuous state space Markov chains. Our methods allow for arbitrary input processes and channel dynamics, provided both have finite memory. We show that the entropy ra...

Specialized classifiers, namely those dedicated to a subset of classes, are often adopted in realworld recognition systems. However, integrating such classifiers is nontrivial. Existing methods, e.g. weighted average, usually implicitly assume that all constituents of an ensemble cover the same set of classes. Such methods can produce misleading predictions when used to combine specialized clas...

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P (.) and ergodic matrix Π is the matrix D ≡ ∫∞ 0 (P (t)−Π)dt. We give conditions for D to exist and discuss properties and a representation of D. The deviation matrix of a birth-death process is investigated in detail. We also describe a new application of deviation matrices by showing that a me...

A reaction network is a chemical system involving multiple reactions and chemical species. The simplest stochastic models of such networks treat the system as a continuous time Markov chain with the state being the number of molecules of each species and with reactions modeled as possible transitions of the chain. This chapter is devoted to the mathematical study of such stochastic models. We b...

We develop a reversible jump Markov chain Monte Carlo approach to estimating the posterior distribution of phylogenies based on aligned DNA/RNA sequences under several hierarchical evolutionary models. Using a proper, yet nontruncated and uninformative prior, we demonstrate the advantages of the Bayesian approach to hypothesis testing and estimation in phylogenetics by comparing different model...

A variety of phenomena are best described using dynamical models which operate on a discrete state space and in continuous time. Examples include Markov (and semiMarkov) jump processes, continuous-time Bayesian networks, renewal processes and other point processes. These continuous-time, discrete-state models are ideal building blocks for Bayesian models in fields such as systems biology, genet...

In this paper, we consider the stochastic generating process—one of the key concepts of the Evolving Transformation System model [1]—from the formal perspective. First, we give an informal definition of the generating process supported by some intuitive assumptions and consider several examples. Then, we formally define the concept of the generating process as a continuous parameter (c.p.) Mark...

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous and multivariate normal, and it is also known that one model class, referred to as models of LWF (Lauritzen–Wermuth–Frydenberg) or block concentration type,...