馬可夫鏈專題

Markov chains are named in honor of the Russian mathematician A. A. Markov, a lover of poetry, who used them to analyze the alternation of vowels and consonants in the poem Eugene Onegin by Pushkin. Markov believed that the only applications of his chains were to the analysis of literary works…

― Howard Anton and Chris Rorres, Elementary Linear Algebra

 

馬可夫鏈簡介：

• 馬可夫過程

無限程序：

• 收斂矩陣
• 廣義收斂矩陣
• Cesàro 矩陣序列
• 譜半徑與矩陣範數

馬可夫矩陣理論：

• 特殊矩陣 (18)：正矩陣
• 特殊矩陣 (20)：可約矩陣
• 特殊矩陣 (21)：非負矩陣

應用實例：

• 應用馬可夫鏈計算擲幣事件發生的機率