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Some Inequalities for the Maximum of Partial Sums of Random Variables

✍ Scribed by J. Mogyoródi

Publisher
John Wiley and Sons
Year
1975
Tongue
English
Weight
623 KB
Volume
70
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

is non-decreasing. Thus, if one applies the c,-inequality, the inequality follows trivially. From this and from the preceding inequality we obtain By our condition the sums on the right hand side converge to 0 as n -+ + 00.

This proves the assertion.

Remarks. It is easy to see that for p > 2 our condition is better than PROKHOROV'S one. For 1 < p 5 2 the condition given in Theorem 4 is better than that of SZYNAL. Examples can be given to show that this is really the situation.

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