Largest excess of boundary crossings for martingales |
| |
Authors: | Prof. Dr. A. Irle |
| |
Affiliation: | 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! |
|