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【正文】 e property 1: all entries ≥ 0. Then we have proved that C is a Markov matrix. At last we use induction and could easily prove the lemma. Markov matrix’ other important properties =1 is an eigenvalue. other eigenvalues, in absolute value, smaller than 1. |λ|1. The voting results of a congressional election are represented by a vector x in R3 If we record the oute of the election every two years by the above vector and the oute of one election depends only on the results of the preceding the sequence of vectors that describe the votes every two years may be a Markov chain. We can take the stochastic matrix P as It means that Determine the likely oute of the next election and the likely oute of the election after that. How to predict the distant future? The most interesting aspect of Markov chains is the study of a chain39。 APPLICATIONS TO MARKOV CHAINS 1211101 1121100210 應(yīng)用物理系 王允磊 What is Markov chains? The Markov chains described in this section are used as mathematical models of a wide variety of situations in biology, business, chemistry, engneering, physics, and elsewhere. In each case, the model is used to describe an experimen
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