We discuss the convergence rates in the law of logarithm for partial sums and randomly indexed partial sums of independent random variables in Banach space, and find the necessary and sufficient conditions on the conv...We discuss the convergence rates in the law of logarithm for partial sums and randomly indexed partial sums of independent random variables in Banach space, and find the necessary and sufficient conditions on the convergence rates. The results of [1-3] for sums of i.i.d. real valued r.v.,s are extended; Yang's[4] result is generalized and the necessity part of Yang's result is also discussed; a conjecture for the i.i.d. real-valued r.v.s. of [5] is answered in Banach space.展开更多
In this paper, we discuss the conditions of complete convergence for partial sums and randomly indexed partial sums of independent but not necessarily identically distributed random elements in type p space, and obtai...In this paper, we discuss the conditions of complete convergence for partial sums and randomly indexed partial sums of independent but not necessarily identically distributed random elements in type p space, and obtain the characterization of Banach space of type p. Yu. H.’s some results(1989) on the case of real value are extended.展开更多
基金This work is supported by the National Natural Science Foundation of China (No.10071081), the Natural Science Foundation of Edu
文摘We discuss the convergence rates in the law of logarithm for partial sums and randomly indexed partial sums of independent random variables in Banach space, and find the necessary and sufficient conditions on the convergence rates. The results of [1-3] for sums of i.i.d. real valued r.v.,s are extended; Yang's[4] result is generalized and the necessity part of Yang's result is also discussed; a conjecture for the i.i.d. real-valued r.v.s. of [5] is answered in Banach space.
文摘In this paper, we discuss the conditions of complete convergence for partial sums and randomly indexed partial sums of independent but not necessarily identically distributed random elements in type p space, and obtain the characterization of Banach space of type p. Yu. H.’s some results(1989) on the case of real value are extended.
