Largest excess of boundary crossings for martingales |
| |
Authors: | Prof Dr A Irle |
| |
Institution: | 1. Mathematisches Seminar, Universit?t Kiel, Olshausenstra?e 40, 2300, Kiel, FRG
|
| |
Abstract: | Summary LetX
1,X
2, ... form a sequence of martingale differences and denote byZ(a, α) = sup n (S
n
−an
α)+ the largest excess forS
n
=X
1 + ... +X
n
crossing the boundaryan
α. We give a sufficient condition for the finiteness ofEZ(a, α)β which is formulated in terms of bounds forE(X
i
+
p
andE(|X
i
|γ|X
1, ...,X
i-1), whereα, β, γ, p are suitably related. This general result is then applied to the case of independent random variables. |
| |
Keywords: | largest excess of boundary crossings martingales martingale inequalities |
本文献已被 SpringerLink 等数据库收录! |
|