Stochastic Models of Mutations and Structural Analysis
This chapter discusses stochastic sequence analysis, which is the mathematical model of pairwise alignment. We start by considering the independent sequence pairs and obtaining the properties of their local correlation functions. Mutations are then divided into two types, depending on when the mutation occurs and the effect of the mutation. These two types are well-described as random walks or processes in mathematics. There are two basic types of random walks, the Bernoulli process and the Poisson process. The counting process and dual renewal process associated with the Bernoulli process and the Poisson process are discussed. In what follows, the random processes of four different mutation types are studied separately. Finally, we generalize the random process under the condition of mixed mutations.
KeywordsStochastic Model Poisson Process Renewal Process Mutation Type Geometric Distribution
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