The goal of branch length estimation in phylogenetic inference is to estimate the divergence time between a set of sequences based on compositional differences between them. A number of software is currently available facilitating branch lengths estimation for homogeneous and stationary evolutionary models. Homogeneity of the evolutionary process imposes fixed rates of evolution throughout the ...

Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {Pn} be a sequence of transition matrices on a finite state space which converge to a limit transition matrix P . Let {Xn} be the associated nonhomogeneous Markov chain where Pn controls movement from tim...

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

The most commonly used models for the failure process of a repairable system are nonhomogeneous Poisson processes, corresponding to minimal repairs, and renewal processes, corresponding to perfect repairs. This paper studies a more general model for recurrent events, called the Trend-Renewal Process (TRP). This is a time transformed renewal process, having both the ordinary renewal process and ...

Abstract. In this research we try to consider the problem of applying the Nonhomogeneous Poisson process to trends of economic development. More specifically, a modified Nonhomogeneous Poisson process is derived when the intensity rate is considered as a solution of stochastic differential equation which satisfies the geometric Brownian motion. The mean and the variance of the modified process ...

Large deviation results are given for a class of perturbed non-homogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {Pn} be a sequence of transition matrices on a finite state space which converge to a limit transition matrix P. Let {Xn} be the associated non-homogeneous Markov chain where Pn controls movement from ti...

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