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INTERSECTIONS AND POLAR FUNCTIONS OF fractional brownian sheetS

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Acta Mathematica Scientia 2008年第4期28卷 779-796页

作者：陈振龙 College of Statistics and Mathematics Zhejiang Gongshang University

Let B^H={B^H（t）,t∈R^N＋}be a real-valued（N,d）fractional brownian sheet with Hurst index H=（H1,…,HN）.The characteristics of the polar functions for B^H are *** relationship between the class of continuous functions satisfying Lipschitz condition and the class of polar-functions of B^H is *** Hausdorff dimension about the fixed points and the inequality about the Kolmogorov’s entropy index for B^H are ***,it is proved that any two independent fractional brownian sheets are nonintersecting in some conditions.A problem proposed by LeGall about the existence of no-polar continuous functions satisfying the Holder condition is also solved.

关键词： fractional brownian sheet polar function Hausdorff dimension intersection

Some Results on fractional brownian sheets and Their Local Times

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Acta Mathematicae Applicatae Sinica 2008年第4期24卷 669-676页

作者： Zong-mao Chen Zheng-yan Lin Institute of Applied Mathematics and Engineering Computation Hangzhou Dianzi University Hangzhou310018 China Department of Mathematics Zhejiang University Hangzhou 310027 China

Let B0^H = {B0^H（t）,t ∈ R＋^N） be a real-valued fractional brownian sheet. Define the （N,d）- Gaussian random field B^H by B^H（t） = （B1^H（t）,...,Bd^H（t）） t ∈ R＋^N, where B1^H, ..., Bd^H are independent copies of B0^H. The existence and joint continuity of local times of B^H is proven in some given conditions in [22]. We then study further properties of the local times of B^H, such as the moments of increments of local times, the large increments and the maximum moduli of continuity of local times and as a result, we answer the questions posed in [22].

关键词： fractional brownian sheet local time Hausdorff measure

fractional 2D-STOCHASTIC CURRENTS

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Acta Mathematica Scientia 2013年第6期33卷 1507-1521页

作者： Ciprian A.TUDOR Maria TUDOR Laboratoire Paul Painlev Universit de Lille 1 F-59655 Villeneuve d’AscqFrance Department of Mathematics Academy of Economical StudiesBucharestRomania

Using multiple stochastic integrals and the stochastic calculus for the frac-tional brownian sheet, we define and we analyze the 2D-fractional stochastic currents.

关键词： currents multiple stochastic integrals fractional brownian sheet two-parameter processes Hurst parameter

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

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Applied Mathematics and Mechanics(English Edition) 2009年第3期30卷 381-390页

作者：林正炎程宗毛 Xing-ming GUO Department of Mathematics Zhejiang University Hangzhou 310028 P. R. China Institute of Applied Mathematics and Engineering Computation Hangzhou Dianzi University Hangzhou 310018 P. R. China 不详

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

关键词： multi-parameter fractional Lévy process fractional brownian sheet local time Gaussian random field multi-parameter Poisson process multi-parameter brownian motion

On intersections of independent anisotropic Gaussian random fields

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Science China Mathematics 2012年第11期55卷 2217-2232页

作者： CHEN ZhenLong XIAO YiMin School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China Department of Statistics and Probability Michigan State UniversityEast Lansing:MI 48824USA

Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional brownian sheets.

关键词： intersection anisotropic Gaussian fields hitting probability Hausdorff dimension stochastic heatequation fractional brownian sheet