Let {X_m} be a sequence of r.v., S, be its partial sum of the first nmembers, and H(t) be a function defined on (0, +∞) with the property of 0 <H(ι)↑+∞ (t→+∞). Denote and ,where ε is an arbitrarily positive ...Let {X_m} be a sequence of r.v., S, be its partial sum of the first nmembers, and H(t) be a function defined on (0, +∞) with the property of 0 <H(ι)↑+∞ (t→+∞). Denote and ,where ε is an arbitrarily positive number. Suppose ψ(t) is another monotone positive function defined on (0, +∞) and (?)(t)=(?)ψ(u)du. lnthis paper, we discuss the relations between the convergence of tail probability series in the law of large numbers and In addition, we obtain a series of equivalent propositions and sufficiet propositions which overall reveal their inner relationships and solve those problems, posed by Soviet scholars recently. It is worth noting that there are some in our correct answers which are different from the forms of their problems.展开更多
文摘Let {X_m} be a sequence of r.v., S, be its partial sum of the first nmembers, and H(t) be a function defined on (0, +∞) with the property of 0 <H(ι)↑+∞ (t→+∞). Denote and ,where ε is an arbitrarily positive number. Suppose ψ(t) is another monotone positive function defined on (0, +∞) and (?)(t)=(?)ψ(u)du. lnthis paper, we discuss the relations between the convergence of tail probability series in the law of large numbers and In addition, we obtain a series of equivalent propositions and sufficiet propositions which overall reveal their inner relationships and solve those problems, posed by Soviet scholars recently. It is worth noting that there are some in our correct answers which are different from the forms of their problems.
