Some Inequalities for Tree Martingales |
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Authors: | Tong-jun He You-liang Hou |
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Institution: | (1) College of Mathematics and Computer Science, Fuzhou University, Fuzhou 35002, China;(2) School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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Abstract: | Abstract
In this paper we study tree martingales and proved that if 1 ≤ α, β < ∞, 1 ≤ p < ∞ then for every predictable tree martingale f = (f
t
, t ∈ T) and Eσ
(P)(f)] < ∞, E S
(P)(f)] < ∞, it holds that where C
αβ
depends only on α and β.
Supported by The National Natural Science Foundation of China (No.10371093) |
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Keywords: | Tree martingale quadratic variation conditional quadratic variation |
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