- 期刊
ON THE WEAK LAW OF LARGE NUMBERS FOR NORMED WEIGHTED SUMS OF I.I.D. RANDOM VARIABLES
並列摘要
For weighted sums (The equation is abbreviated) of independent and identically distributed random variables {Y_n,n≥1}, a general weak law of large numbers of the form (The equation is abbreviated) is established where {ν_n,n≥1} and {b_n,n≥1} are suitable constants. The hypotheses involve both the behavior of the tail of the distribution of |Y_1| and the growth behaviors of the constants {a_n,n≥1} and {b_n,n≥1}. Moreover, a weak law is proved for weighted sums (The equation is abbreviated) indexed by random variables {T_n,n≥1}. An example is presented wherein the weak law holds but the strong law fails thereby generalizing a classical example.
延伸閱讀
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