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
A Kolmogorov inequality for the sum of independent Bernoulli random variables with unequal means
โ Scribed by Danny W. Turner; Dean M. Young; John W. Seaman Jr.
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 109 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let X be a random variable satisfying for some z =-0. \Ye denote by P ( x ) the distribution function, by f ( t ) the characteristic function of the random variable X and introduce such that l a / -= ~/ 3 because of (1). Further, we use the denotations
Let \(\left\{X, X_{n} ; \vec{n} \in \mathbb{N}^{d}\right\}\) be a field of independent identically distributed real random variables, \(0<p<2\), and \(\left\{a_{\bar{n}, \bar{k}} ;(\bar{n}, \bar{k}) \in \mathbb{N}^{d} \times \mathbb{N}^{d}, \bar{k} \leqslant \bar{n}\right\}\) a triangular array of r