WOLFRAM

Wolfram 语言与系统参考资料中心

有限马可夫过程的平稳分布

    
找到连续马可夫过程的平稳分布：
Wolfram Language code: StationaryDistribution[ContinuousMarkovProcess[1, {{-a, a}, {b, -b}}]]
执行在平稳分布上的操作：
Wolfram Language code: Mean[%]//Simplify
找到离散马可夫过程的平稳分布和其均值：
Wolfram Language code: StationaryDistribution[DiscreteMarkovProcess[1, {{a, 1 - a}, {1 - b, b}}]]
Wolfram Language code: Mean[%]//Simplify
Wolfram Language code: DiscretePlot[PDF[StationaryDistribution[With[{λ = 4, μ = 60 / 12, m = 10 ^ 2}, ContinuousMarkovProcess[1, SparseArray[Join[Table[{i, i + 1} -> λ, {i, m}], Table[{i + 1, i} -> μ, {i, m}], Table[{i, i} -> -λ - μ, {i, 2, m}], {{1, 1} -> -λ, {m + 1, m + 1} -> -μ}]]]]], k], {k, 1, 20}, ExtentSize -> 0.5, PlotRange -> All]