A note on the domination inequalities and their applications

作者：Ren, Yaofeng^*; Shen, Jing

来源：Statistics & Probability Letters, 2012, 82(6): 1160-1168.

DOI：10.1016/j.spl.2012.03.002

• Domination inequality
• Increasing process
• Locally square integrable martingale
• Ornstein-Uhlenbeck process
• Bessel process

In this note, we present some refinements of the well-known domination inequalities. Let X be an adapted positive cadlag process dominated by a predictable increasing process A with A(0) = 0. We derive some sharper constants in the inequalities. For the widely used inequality
E [(X-infinity*)(p)] <= 2 - p/1 - pE (A(infinity)(p)), 0 < p < 1,
we obtain the following strengthened version
E [(X-infinity*)(p)] <= 1/1 - p (1/p)(p) E (A(infinity)(p)), 0 < p < 1.
Where X-infinity* = sup(t 0(+) in the following L-p inequality:
parallel to X-infinity*parallel to(p) <= C-p parallel to A(infinity)parallel to(p), 0 < p < 1.
We also apply the improved inequalities to martingales. the Ornstein-Uhlenbeck process and Bessel processes.

• 出版日期2012-6
• 单位中国人民解放军海军工程大学