MARKOV CHAINS: BASIC THEORY
A stochastic matrix is a square nonnegative matrix all of whose row sums are 1. A substochastic matrix is a square nonnegative matrix all of whose row sums are 1. A doubly stochastic matrix is a stochastic matrix all of whose column sums are 1. Observe that if you start with a stochastic matrix and delete the rows and columns indexed
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CONDITIONAL EXPECTATION AND MARTINGALES
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