Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋·...Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋···＋（Std）2）~1/2 is the sub-fractional Bessel process.展开更多
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 （A↓t≥0）. Then we establish the relationship between L^p-norm o...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 （A↓t≥0）. Then we establish the relationship between L^p-norm of log^1/2（1 ＋δJτ） and L^p-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 ｜｜log^1/2（1＋δLm＋1（τ）｜｜p and ｜｜supZtП[1＋Lj（t]^1/2｜｜p （0≤j≤m,j∈Z;0≤t≤τ） are equivalent with 0〈p〈＋∞ for all stopping times rand 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.展开更多
By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/xs（v） is studied, where （Xt（v）, t ≥0） is a squared Bessel process with index v 〉 0. Xs The rate function can be given expl...By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/xs（v） is studied, where （Xt（v）, t ≥0） is a squared Bessel process with index v 〉 0. Xs The rate function can be given explicitly. Furthermore, the functional moderate deviations for the Bessel clock are obtained.展开更多
For a transient Bessel process X let I(t) = in fs＞tX(s) and§(t) = inf{u≥ 2 t: X(u) = I(t)}. In this note we compute the joint distribution of I(t),§(t) and Xt.
The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an os- cillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies...The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an os- cillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel.展开更多
基金Supported by the NSFC (10871041)Key NSF of Anhui Educational Committe (KJ2011A139)
文摘Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋···＋（Std）2）~1/2 is the sub-fractional Bessel process.
基金Project supported by the National Natural Science Foundation of China (No. 10571025) and the Key Project of Chinese Ministry of Education (No. 106076)
文摘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 （A↓t≥0）. Then we establish the relationship between L^p-norm of log^1/2（1 ＋δJτ） and L^p-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 ｜｜log^1/2（1＋δLm＋1（τ）｜｜p and ｜｜supZtП[1＋Lj（t]^1/2｜｜p （0≤j≤m,j∈Z;0≤t≤τ） are equivalent with 0〈p〈＋∞ for all stopping times rand 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.
基金Research supported by the National Natural Science Foundation of China(10871153)funded by the Revitalization Project of Zhongnan University of Economics and Law
文摘By the method of change measures, the moderate deviations for the Bessel clock ∫t0ds/xs（v） is studied, where （Xt（v）, t ≥0） is a squared Bessel process with index v 〉 0. Xs The rate function can be given explicitly. Furthermore, the functional moderate deviations for the Bessel clock are obtained.
基金Supported by National Natural Science Foundation of China (19801020)
文摘For a transient Bessel process X let I(t) = in fs＞tX(s) and§(t) = inf{u≥ 2 t: X(u) = I(t)}. In this note we compute the joint distribution of I(t),§(t) and Xt.
基金supported by MNiSW(Grant No.N201 417839)supported by(Grant No.MTM2012-36732-C03-02)from Spanish Government
文摘The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an os- cillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel.
