Stochastic

What is the probability that the line of a man

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Unformatted text preview: .e., the branching process becomes absorbed at 0? Reverend Henry William Watson replied with a solution. Together, they then wrote an 1874 paper entitled On the probability of extinction of families. For this reason, these chains are often called Galton-Watson processes. Example 1.9. Wright–Fisher model. Thinking of a population of N/2 diploid individuals who have two copies of each of their chromosomes, or of N haploid individuals who have one copy, we consider a fixed population of N genes that can be one of two types: A or a. In the simplest version of this model the population at time n + 1 is obtained by drawing with replacement from the population at time n. In this case, if we let Xn be the number of A alleles at time n, then Xn is a Markov chain with transition probability ✓ ◆ ✓ ◆j ✓ ◆N j N i i p(i, j ) = 1 N N j since the right-hand side is the binomial distribution for N independent trials with success probability i/N . 6 CHAPTER 1. MARKOV CHAINS In this model t...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

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