紀要論文 The Conditional Strong Law of Large Numbers in Separable Banach Spaces

Shikimi, Takuhisa

97 ( 1-4 )  , pp.61 - 70 , 2018-01-25 , 長崎大学経済学会
ISSN:02869101
内容記述
Let X be a separable Banach space. Suppose that X1, X2,... are X valued random variables that are conditionally independent and identically distributed given a sub-σ-algebra. We show that, conditional on the sub-σ-algebra, n-1Σni=1 Xi converges to the conditional expectation of X1 a.s.
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http://naosite.lb.nagasaki-u.ac.jp/dspace/bitstream/10069/37967/1/Keizai97_1_61.pdf

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