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- W2078554058 abstract "This paper contains a general dependent extension of Doob's inequality for martingales, $E(max_{ileqq n} S_i^2) leqq 4ES_n^2$. This inequality is then used to extend the martingale convergence theorem for $L_2$ bounded variables, and to prove strong laws under dependent assumptions. Strong and $varphi$-mixing variables are shown to satisfy the conditions of these theorems and hence strong laws are proved as well for these." @default.
- W2078554058 created "2016-06-24" @default.
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- W2078554058 date "1975-10-01" @default.
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- W2078554058 title "A Maximal Inequality and Dependent Strong Laws" @default.
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- W2078554058 doi "https://doi.org/10.1214/aop/1176996269" @default.
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