MAT 1302 Lecture Notes - Lecture 23: Dynamical System, Probability Vector, Free Variables And Bound Variables

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Markov chains: dynamical systems whose state changes over time. They consist of a number of variables that are put together as a single vector, the state vector. Important: in markov chains, the variables add up to 1. https://www. datacamp. com/community/tutorials/markov-chains-python-tutorial. Stochastic matrix: a matrix such that such that every column is a probability vector. Important: if v is a probability vector and p is stochastic then pv is a probability vector and a stochastic matrix for any k. Markov chain: is a sequence of probability vectors together with a stochastic matrix. is are nonzero. Long term trend: we assume that the conditions remain the same from year to year. Without a spreadsheet, compute the long term trend with a vector v such that pv = v. Regularity: a stochastic matrix is regular if all entries of. 1- there is a unique probability vector v such that pv = v. 2- 1 is an eigenvalue of p and v is an associated eigenvector.

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