馬爾科夫過(guò)程介紹ppt課件-閱讀頁(yè)
2025-05-22 12:05本頁(yè)面
【正文】 P How to get the steadystate vector? We choose a basis for the solution space. A simple choice is To make it as a steadystate vector, we divide w by the sum of its entries and obtain The book has this sentence: “It can be shown that every stochastic matrix has a steadystate vector for P”. Next we will prove this claim. Proof: Let M=PI and let M= For matrix P, we know that the columns of P are probability vectors. So the sum of elements of every column vector of P is 1. Obviously, the sum of elements of every column vector of M is means that So the row vectors of matrix M are linear dependent. So the determinant of matrix M is the nature of the equation MX=0 we just prove its solution space isn’t zero. ??????????321???0321 ??? ???DEFINITION: say that a stochastic matrix is regular if some matrix power Pk contains only strictly positive entries. say that a sequence of vectors converges to a vector if the entries in xk can be made as close as desired to the corresponding entries in q by taking k sufficiently large. 一般的馬爾科夫過(guò)程
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