共查询到19条相似文献,搜索用时 93 毫秒
1.
2.
本文利用白噪声分析方法研究了两个相互独立的多分数布朗运动的碰撞局部时问题.首先分别讨论了碰撞局部时在Hida广义泛函空间和L~2空间中的存在性.进一步,利用多分数布朗运动的局部不确定性获得了该局部时的正则性条件. 相似文献
3.
本文在经典白噪声分析框架下,用一种新的方法研究随机流动形. 首先使用布朗运动的Wick积分定义Wick型随机流动形.进一步, 用白噪声分析方法和S-变换证明:布朗随机流动形可视为Hida广义泛函. 相似文献
4.
在白噪声分析的框架中,我们给出了广义Weiner泛函空间上的梯度算子和散度算子的定义与公式,并利用梯度和散度算子以及适应投影建立了广义泛函的表示公式.也证明了积分核算子可用梯度与散度算子表出. 相似文献
5.
6.
本文利用经典的白噪声分析框架研究布朗运动和分数布朗运动混合的局部时.利用白噪声分析方法证明该局部时是一个Hida广义泛函.进一步,借助于S-变换给出了该局部时的混沌表示.本文所获得结果推广了GUO等(2011)获得的分数布朗运动情形下的一些结果. 相似文献
7.
8.
9.
在白噪声分析框架下构造了λ44广义泛函,定义了其相应的Schwinger函数,验证了它满足除反射正性之外的全部OS公理,并回顾了Euclid随机场理论的进展和一些问题. 相似文献
10.
本文建立了Banach空间中无界时滞的脉冲发展中立泛函积分微分包含温和解存在的充分条件,我们利用由Dhage建立的多值混合不动点定理与发展系统证明了解的存在性. 相似文献
11.
Cai Shi WANG Zhi Yuan HUANG 《数学学报(英文版)》2006,22(1):157-168
Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals. 相似文献
12.
?B-值广义泛函值函数可微性的刻画 总被引:2,自引:0,他引:2
In this paper, we discuss fuzzy simplex and fuzzy convex hull, and give several representation theorems for fuzzy simplex and fuzzy convex hull. In addition, by giving a new characterization theorem of fuzzy convex hull, we improve some known results about fuzzy convex hull. 相似文献
13.
Jan Maas 《Journal of Mathematical Analysis and Applications》2010,363(2):383-398
We develop a theory of Malliavin calculus for Banach space-valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Itô isometry to Banach spaces. In the white noise case we obtain two sided Lp-estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener-Itô chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the opposite direction we use Meyer's inequalities to give a new proof of a decoupling result for Gaussian chaoses in UMD Banach spaces. 相似文献
14.
Employing the Segal-Bargmann transform (S-transform for abbreviation) of regular Lévy white noise functionals, we define and study the generalized Lévy white noise functionals by means of their functional representations acting on test functionals. The main results generalize (Gaussian) white noise analysis initiated by T. Hida to non-Gaussian cases. Thanks to the closed form of the S-transform of Lévy white noise functionals obtained in our previous paper, we are able to define and study the renormalization of products of Lévy white noises, multiplication operator by Lévy white noises, and the differential operators with respect to a Lévy white noise and their adjoint operators. In the courses of our investigation we also obtain a formula for the products of multiple Lévy-Itô stochastic integrals. As applications, we discuss the existence of Hitsuda-Skorokhod integral for Lévy processes, Kubo-Takenaka formula for Lévy processes, and Itô formula for generalized Lévy white noise functionals. 相似文献
15.
Neil E. Gretsky 《Annali di Matematica Pura ed Applicata》1974,101(1):337-354
Summary The notation of Gramian matrix is generalized to operators between function spaces and then used to provide an operator-valued
inner product between pairs of Hilbert space-valued Banach function spaces. In this context projection operators, Schwarz's
inequality, and orthonormal series are discussed.
Entrata in Redazione il 26 marzo 1973. 相似文献
16.
在实Schwartz广义函数空间上,证明了复值广义维纳泛函,由Kondratev-Streit及Hida构造的复值白噪声分布都是由Khrennikov构造的分布。利用上述结果进而证明了,一类无穷维伪微分算子是由复值广义维纳泛函空间上的连续线性算子族扩张而成。更进一步,还证明了由Khrennikov构造的关于分布的试验函数空间是关于白噪声泛函的Meyer-Yan试验函数空间的子空间。 相似文献
17.
In this paper, we establish asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths under the condition that the phase function has finitely many non-degenerate minima. Our main tool is the Banach space-valued rough path theory of T. Lyons. We use a large deviation principle and the stochastic Taylor expansion with respect to the topology of the space of geometric rough paths. This is a continuation of a series of papers by Inahama [Y. Inahama, Laplace's method for the laws of heat processes on loop spaces, J. Funct. Anal. 232 (2006) 148-194] and by Inahama and Kawabi [Y. Inahama, H. Kawabi, Large deviations for heat kernel measures on loop spaces via rough paths, J. London Math. Soc. 73 (3) (2006) 797-816], [Y. Inahama, H. Kawabi, On asymptotics of certain Banach space-valued Itô functionals of Brownian rough paths, in: Proceedings of the Abel Symposium 2005, Stochastic Analysis and Applications, A Symposium in Honor of Kiyosi Itô, Springer, Berlin, in press. Available at: http://www.abelprisen.no/no/abelprisen/deltagere_2005.html]. 相似文献
18.
De Sheng Yang 《数学学报(英文版)》2010,26(8):1601-1612
This paper proves the existence and uniqueness of solutions in a Banach space for the generalized stochastic Ginzburg-Landau equation with a multiplicative noise in two spatial dimensions. The noise is white in time and correlated in spatial variables. The condition on the parameters is the same as in the deterministic case. The Banach contraction principle and stochastic estimates in Banach spaces are used as the main tool. 相似文献
19.
S.V. LototskyB.L. Rozovskii D. Seleši 《Stochastic Processes and their Applications》2012,122(3):808-843
The Malliavin derivative, the divergence operator (Skorokhod integral), and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to nonlinear generalized functionals of white noise. These extensions are related to the new developments in the theory of stochastic PDEs, in particular elliptic PDEs driven by spatial white noise and quantized nonlinear equations. 相似文献