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Journal of Zhejiang University SCIENCE A 2007 Vol.8 No.1 P.158~163

http://doi.org/10.1631/jzus.2007.A0158


Lp-estimates on a ratio involving a Bessel process


Author(s):  LU Li-gang, YAN Li-tan, XIANG Li-chi

Affiliation(s):  Basic College, Zhejiang Wanli University, Ningbo 315101, China; more

Corresponding email(s):   luligang1234@126.com

Key Words:  Bessel processes, Diffusion process, Itô, &rsquo, s formula, Domination relation


LU Li-gang, YAN Li-tan, XIANG Li-chi. Lp-estimates on a ratio involving a Bessel process[J]. Journal of Zhejiang University Science A, 2007, 8(1): 158~163.

@article{title="Lp-estimates on a ratio involving a Bessel process",
author="LU Li-gang, YAN Li-tan, XIANG Li-chi",
journal="Journal of Zhejiang University Science A",
volume="8",
number="1",
pages="158~163",
year="2007",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2007.A0158"
}

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%D 2007
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%DOI 10.1631/jzus.2007.A0158

TY - JOUR
T1 - Lp-estimates on a ratio involving a Bessel process
A1 - LU Li-gang
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A1 - XIANG Li-chi
J0 - Journal of Zhejiang University Science A
VL - 8
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EP - 163
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.2007.A0158


Abstract: 
Let Z=(Zt)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 Lp-norm of log1/2(1+δJτ) and Lp-norm of sup Zt[t+k(t)]–1/2 (0≤tτ) for all stopping times τ and all 0<p<+∞. As an interesting example, we show that ||log1/2(1+δLm+1(τ))||p and ||supZt∏[1+Lj(t)]–1/2||p (0≤jm, j∈Ζ; 0≤tτ) are equivalent with 0<p<+∞ for all stopping times τ and all integer numbers m, where the function Lm(t) (t≥0) is inductively defined by Lm+1(t)=log[1+Lm(t)] with L0(t)=1.

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Reference

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