Exact inequalities for sums of asymmetric random variables, with applications
β Scribed by Iosif Pinelis
- Publisher
- Springer
- Year
- 2007
- Tongue
- English
- Weight
- 475 KB
- Volume
- 139
- Category
- Article
- ISSN
- 1432-2064
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
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 c
We give a comparison inequality that allows one to estimate the tail probabilities of sums of independent Banach space valued random variables in terms of those of independent identically distributed random variables. More precisely, let X 1 X n be independent Banach-valued random variables. Let I