In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient cond...In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient condition for the existence of the derivatives,which makes us obtain the exponential integrability and H?lder continuity.Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin.Moreover,we also study the power variation of the derivatives.展开更多
This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, co...This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.展开更多
Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ...Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.展开更多
Let Sdp be the p-multiple time set of the Brownian motion in d dimensions. In this paper , the Hausdorff measure function for S32 is proved to be , and the Hausdorff measuure problem for S2p is also discussed. As a re...Let Sdp be the p-multiple time set of the Brownian motion in d dimensions. In this paper , the Hausdorff measure function for S32 is proved to be , and the Hausdorff measuure problem for S2p is also discussed. As a result, a conjecture suggested by J. Rosen is partially proved.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.12071003,12201294)Natural Science Foundation of Jiangsu Province,China(Grant No.BK20220865)。
文摘In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient condition for the existence of the derivatives,which makes us obtain the exponential integrability and H?lder continuity.Then we show that this condition is also necessary for the existence of derivatives of intersection local time at the origin.Moreover,we also study the power variation of the derivatives.
基金Research of Z. Chen and D. Wu was partially supported by the National Natural Science Foundation of China （Grant No. 11371321）. Research of Y. Xiao was partially supported by the NSF Grants DMS-1307470 and DMS-1309856.
文摘This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.
基金supported by National Natural Science Foundation of China (Grant No.10871041)Key Natural Science Foundation of Anhui Educational Committee (Grant No. KJ2011A139)
文摘Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.
文摘Let Sdp be the p-multiple time set of the Brownian motion in d dimensions. In this paper , the Hausdorff measure function for S32 is proved to be , and the Hausdorff measuure problem for S2p is also discussed. As a result, a conjecture suggested by J. Rosen is partially proved.
