Abstract. Under a markovian evolutionary process, the expected number of substitutions per site (also called branch length) that have occurred when a sequence has evolved from another according to a transition matrix P can be approximated by − 1 4 log detP. When the Markov process is assumed to be continuous in time, i.e. P = expQt it is easy to simulate this evolutionary process for a given br...

investors use different approaches to select optimal portfolio. so, optimal investment choices according to return can be interpreted in different models. the traditional approach to allocate portfolio selection called a mean - variance explains. another approach is markov chain. markov chain is a random process without memory. this means that the conditional probability distribution of the nex...

An algorithm for estimation of the parameters of a multiscale stochastic process based on scale-recursive dynamics on trees is presented. The expectation-maximization algorithm is used to provide maximum likelihood estimates for the general case of a nonhomogeneous tree with no fixed structure for the process dynamics. Experimental results are presented using synthetic data.

Process adjustment, also known as process targeting, is one of the classical problems in the field of quality control and production economics. In the process adjustment problem, it is assumed that process parameters are variables and the aim is to determine these parameters such that certain economic criteria are optimally satisfied. The aim of this paper is to determine the optimal process ad...

In this paper at rst, a history of mathematical models is given.Next, some basic information about random variables, stochastic processesand Markov chains is introduced. As follows, the entropy for a discrete timeMarkov process is mentioned. After that, the entropy for SIS stochastic modelsis computed, and it is proved that an epidemic will be disappeared after a longtime.