|
|
|
题名
|
作者
|
年代
|
出处
|
被引量
|
| 1 | The generalized Bouleau-Yor identity for a sub-fractional Brownian motion显示文摘Let SH be a sub-fractional Brownian motion with index 0 < H < 1/2.In this paper we study the existence of the generalized quadratic covariation [f(SH),SH](W) defned by[f(SH), SH](W)t= limε→01/ε2H∫t0{f(SHs+ε)-f(SHs)}(SHs+ε-SHs)ds2H,provided the limit exists in probability, where x → f(x) is a measurable function. We construct a Banach space ■ of measurable functions such that the generalized quadratic covariation exists in L2 provided f ∈ H.Moreover, the generalized Bouleau-Yor identity takes the form ∫Rf(x)ψH(dx, t) =(2-22H-1)[f(SH), SH](W)t for all f∈■, where ψH(x, t) is the weighted local time of SH. This allows us to write the generalized It's formula for absolutely continuous functions with derivative belonging to | YAN LiTan HE Kun CHEN Chao | 2013 | Science China Mathematics2013，56，10： | 9 |
| 2 | Smoothness of local times and self-intersection local times of Gaussian random fields显示文摘这份报纸涉及光滑(在 Meyer-Watanabe 的意义) Gaussian 随机的地的本地时间。为时间,碰撞本地人时间,和本地的自我交叉预定的本地人的存在和光滑的足够、必要的条件为 Gaussian 随机的域的一个大类被建立,包括部分 Brownian 运动,部分 Brownian 表和时空 Gaussian 噪音驾驶的随机的热方程的解决方案。 | Zhenlong CHEN DongshengWU Yimin XIAO | 2015 | Frontiers of Mathematics in China2015，10，4： | 3 |
| 3 | 时空各向异性Gauss场的碰撞概率和维数显示文摘设X={X(t)∈R^d,t∈R^N}是一个零均值的时空各向异性的Gauss随机场,ρ和τ分别是在R^N和R^d上引进的两个各向异性的时空度量.在某些一般条件下,本文通过τ下的Hausdorff测度和容度,分别给出了X碰撞概率的上、下界.同时,在ρ、τ和Euclid度量下,本文分别得到了又的像集、图集、逆像集和水平集的Hausdorff维数和填充维数.这些结果包含和推广了现有的仅在时间上各向异性的一类Gauss随机场的相关结果. | 倪文清 陈振龙 | 2018 | 中国科学:数学2018，48，3： | 2 |
| 4 | ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES显示文摘Let X(1)= {X(1)(s), s ∈ R+ } and X(2)= {X(2)(t), t ∈ R+ } be two independent nondegenerate diusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X(1)and X(2)are studied. More generally, let E1, E2 ■(0, ∞) and F Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1) ∩ X(2)(E2) ∩ F = φ} > 0 are proved in terms of the Bessel-Riesz type capacity and Hausdor measure of E1 ×E2 ×F in the metric space(R+ ×R+ ×Rd, ρ), where ρ is an unsymmetric metric defined in R+ × R+ × Rd. Under reasonable conditions, results resembling those of Browian motion are obtained. | 陈振龙 | 2014 | Acta Mathematica Scientia2014，34，1： | 1 |
| 5 | Hitting Probabilities and the Hausdorff Dimension of the Inverse Images of a Class of Anisotropic Random Fields显示文摘Let X = {X(t):t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields. | Zhen Long CHEN Quan ZHOU | 2015 | Acta Mathematica Sinica,English Series2015，31，12： | 1 |
| 6 | 独立随机场的多重相交性与Hausdorff维数显示文摘设X^H={X^H(s),s∈R^(N1)}和X^K={X^K(t),t∈R^(N2)}是指数分别为H∈(0,1)^(N1)和K∈(0,1)^(N2)、取值于R^d的两个独立的各向异性随机场,它们可以不具有Gauss性.在某些一般条件下,本文研究了X^H和X^K的样本轨道相交的存在性.更一般地,对任意的Borel集F?R^d,本文给出了F包含X^H和X^K相交点的一些充分和必要条件,确定了X^H与X^K在F中的相交时集的Hausdorff维数.这些结果适用于带有乘性噪声的非线性随机热方程的非Gauss解和双分数Brown单. | 陈振龙 | 2016 | 中国科学:数学2016，46，9： | 1 |
| 7 | HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS显示文摘Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations. | 王军 陈振龙 | 2022 | Acta Mathematica Scientia2022，42，2： | 0 |
| 8 | 空间各向异性Gauss场的局部时和逆像集的维数 献给余家荣教授100华诞显示文摘本文研究一类在空间R^d中具有各向异性的(N, d)-Gauss随机场,证明其局部时的正则性和逆像集的Hausdorff维数的新结果.本文也给出(N, d)-Gauss随机场的一些公开问题. | 陈振龙 肖益民 | 2019 | 中国科学:数学2019，49，11： | 0 |
| 9 | 分数布朗单的幂函数随机积分逼近(英文)显示文摘本文研究了分数布朗单的逼近问题.利用Wiener积分,得到了分数布朗单的幂函数型随机积分逼近. | 桑利恒 申广君 夏良文 | 2017 | 数学杂志2017，37，1： | 0 |
| 10 | Besov空间上Riemann-Liouville型重分数布朗单的弱收敛(英文)显示文摘本文研究Besov空间上Riemann-Liouville型重分数布朗单的弱收敛问题.分别利用平面上的Poisson过程和两列独立的Riemann-Liouville型重分数布朗运动的部分和,构造了Riemann-Liouville型重分数布朗单的弱极限定理. | 桑利恒 申广君 戴洪帅 | 2016 | 应用数学2016，29，4： | 0 |
您所在的机构暂未开通此部分的功能，请联系管理员