| L^p-estimates on a ratio involving a Bessel process |
| |
| 作者姓名： | LU Li-gang YAN Li-tan XIANG Li-chi |
| |
| 作者单位： | LU Li-gang1，YAN Li-tan 2，XIANG Li-chi1 (1Basic College，Zhejiang Wanli University，Ningbo 315101，China) (2Department of Mathematics，College of Science，Donghua University，Shanghai 200051，China) |
| |
| 基金项目： | Project supported by the National Natural Science Foundation of China (No. 10571025) and the Key Project of Chinese Ministry of Education (No. 106076) |
| |
| 摘 要： | INTRODUCTION Throughout this paper, we shall work with a filtered complete probability space (?,F,(Ft),P) sat-isfying the usual conditions. Let B=(Bt)t≥0 be a stan-dard Brownian motion with B0=0. Denote by ú the set of all non-negative real numbers. Recall that a diffusion process X starting at x≥0 is called the square of a Bessel process of dimension δ>0 if d X t = δd t 2 | X t |d Bt , X 0= x, (1) Clearly, this equation has a unique non-negative strong solution X, i.e., …
|
| 关 键 词： | Bessel processes Diffusion process It’s formula Domination relation |
| 收稿时间： | 2006-03-03 |
| 修稿时间： | 2006-08-09 |
L
p
-estimates on a ratio involving a Bessel process |
| |
| LU Li-gang YAN Li-tan XIANG Li-chi.L^p-estimates on a ratio involving a Bessel process[J].Journal of Zhejiang University Science,2007,8(1):158-163. |
| |
| Authors: | Li-gang Lu Li-tan Yan Li-chi Xiang |
| |
| Institution: | (1) Basic College, Zhejiang Wanli University, Ningbo, 315101, China;(2) Department of Mathematics, College of Science, Donghua University, Shanghai, 200051, China |
| |
| Abstract: | Let Z=(Z
t
)
t≥0 be a Bessel process of dimension δ(δ>0) starting at zero and let K(t) be a differentiable function on 0, ∞) with K(t)>0 (∀t≥0). Then we establish the relationship between L
p
-norm of log1/2(1+δJ
τ) and L
p
-norm of sup Z
t
t+k(t)]−1/2 (0≤t≤τ) for all stopping times τ and all 0<p<+∞. As an interesting example, we show that ‖log1/2(1+δL
m+1(τ))‖
p
and ‖supZ
t
Π1+L
j
(t]−1/2‖
p
(0≤j≤m,j∈ —; 0≤t≤τ) are equivalent with 0<p<+∞ for all stopping times τ and all integer numbers m, where the function L
m
(t) (t≥0) is inductively defined by L
m+1(t)=log1+L
m
(t)] with L
0(t)=1.
Project supported by the National Natural Science Foundation of China (No. 10571025) and the Key Project of Chinese Ministry
of Education (No. 106076) |
| |
| Keywords: | Bessel processes Diffusion process It(o)'s formula Domination relation |
| 本文献已被 CNKI 维普 SpringerLink 等数据库收录！ |
