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On-line Access: 2024-08-27
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Lp-estimates on a ratio involving a Bessel process
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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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%T Lp-estimates on a ratio involving a Bessel process
%A LU Li-gang
%A YAN Li-tan
%A XIANG Li-chi
%J Journal of Zhejiang University SCIENCE A
%V 8
%N 1
%P 158-163
%@ 1673-565X
%D 2007
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2007.A0158
TY - JOUR
T1 - Lp-estimates on a ratio involving a Bessel process
A1 - LU Li-gang
A1 - YAN Li-tan
A1 - XIANG Li-chi
J0 - Journal of Zhejiang University Science A
VL - 8
IS - 1
SP - 158
EP - 163
%@ 1673-565X
Y1 - 2007
PB - Zhejiang University Press & Springer
ER -
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≤t≤τ) 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≤j≤m, j∈Ζ; 0≤t≤τ) 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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