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Local times of linear multifractional stable sheets
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作者 SHEN Guang-jun YU Qian LI Yun-meng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2020年第1期1-15,共15页
Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existen... Let X^H(u)(u)={X^H(u)(u);u∈R^N+}be linear multifractional stable sheets with index functional H(u),where H(u)=(H1(u),…,HN(u))is a function with values in(0;1)N.Based on some assumptions of H(u),we obtain the existence of the local times of X^H(u)(u)and establish its joint continuity and the Holder regularity.These results generalize the corresponding results about fractional stable sheets to multifractional stable sheets. 展开更多
关键词 multifractional stable sheets local nondeterminism local times joint continuity
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Self-intersection local times and collision local times of bifractional Brownian motions 被引量:12
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作者 JIANG YiMing WANG YongJin 《Science China Mathematics》 SCIE 2009年第9期1905-1919,共15页
In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the ex... In this paper, we consider the local time and the self-intersection local time for a bifractional Brownian motion, and the collision local time for two independent bifractional Brownian motions. We mainly prove the existence and smoothness of the self-intersection local time and the collision local time, through the strong local nondeterminism of bifractional Brownian motion, L2 convergence and Chaos expansion. 展开更多
关键词 bifractional Brownian motion self-intersection local time collision local time strong local nondeterminism 60G15 60G18 60J55
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Uniform dimension results for Gaussian random fields 被引量:6
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作者 WU DongSheng XIAO YiMin 《Science China Mathematics》 SCIE 2009年第7期1478-1496,共19页
Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their conne... Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed. It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an (N, d)-Gaussian random field as in (1), where X 1,...,X d are independent copies of a real valued, centered Gaussian random field X 0 which is anisotropic in the time variable. We establish uniform Hausdorff dimension results for the image sets of X. These results extend the corresponding results on one-dimensional Brownian motion, fractional Brownian motion and the Brownian sheet. 展开更多
关键词 anisotropic Gaussian random fields sectorial local nondeterminism IMAGE Hausdorff dimension 60G15 60G17 60G60 42B10 43A46 28A80
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Dimensional Properties of Fractional Brownian Motion 被引量:1
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作者 Dong Sheng WU Yi Min XIAO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第4期613-622,共10页
Let B^α = {B^α(t),t E R^N} be an (N,d)-fractional Brownian motion with Hurst index α∈ (0, 1). By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension result... Let B^α = {B^α(t),t E R^N} be an (N,d)-fractional Brownian motion with Hurst index α∈ (0, 1). By applying the strong local nondeterminism of B^α, we prove certain forms of uniform Hausdorff dimension results for the images of B^α when N 〉 αd. Our results extend those of Kaufman for one-dimensional Brownian motion. 展开更多
关键词 fractional Brownian motion Hausdorff dimension uniform dimension results strong local nondeterminism
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