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The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to $\left({0,\infty } \right)$ instead of $\left( {0,2} \right)$, we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.
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참고문헌 (22)
참고문헌 신청
L. E. Baum / 1965 / Convergence rates in the law of large numbers / Trans. Amer. Math. Soc 120(1):108~123
Y. S. Chow / 1973 / Delayed sums and Borel summability of independent, identically distributed random variables / Bull. Inst. Math. Acad. Sinica 1(2):207~220
Y. S. Chow / 1997 / Probability Theory: Independence, Interchangeability, Martingales / Springer-Verlag
T. C. Christofides / 2013 / Conditional demimartingales and related results / J. Math. Anal. Appl 398(1):380~391
P. Erd¨os / 1949 / On a theorem of Hsu and Robbins / Ann. Math. Statist 20(2):286~291
Y. S. Chow / 1973 / Delayed sums and Borel summability of independent, identically distributed random variables / Bull. Inst. Math. Acad. Sinica 1(2):207~220
Y. S. Chow / 1997 / Probability Theory: Independence, Interchangeability, Martingales / Springer-Verlag
T. C. Christofides / 2013 / Conditional demimartingales and related results / J. Math. Anal. Appl 398(1):380~391
P. Erd¨os / 1949 / On a theorem of Hsu and Robbins / Ann. Math. Statist 20(2):286~291
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