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白噪声分析中的Bochner-Wick积分 被引量:4

The Bochner-Wick Integrals On White Noise Space
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摘要 本文对取值于广义Wiener泛函空间(S)的向量值测度P,定义了一种Wick积分,给出了Wick积分存在的充要条件,并说明了这种积分不仅是Boch(?)积分的推广,而且是Skrochod积分的推广,最后研究了Bochner-Wick积分的Fubini定理。 In this paper, we define a kind of Bochner-Wick integral for vector measure which takes value in the space of generalized Wiener functionals and give sufficient and necessary conditions for the integrablity. In the end, we discuss corresponding Fubini theorm which is the generalization of that of integral about Brownian motion.
作者 宁克标
机构地区 华东师范大学
出处 《应用概率统计》 CSCD 北大核心 1996年第3期239-246,共8页 Chinese Journal of Applied Probability and Statistics
基金 国家自然科学基金资助项目
  • 相关文献

参考文献3

  • 1He S W,1994年
  • 2Huang Z Y,Gaussian Random Fields,1991年
  • 3夏道行,泛函分析第二教程,1987年

同被引文献16

  • 1王湘君,王才士.广义算子值函数可微性的刻画[J].数学物理学报(A辑),2004,24(4):454-458. 被引量:1
  • 2Cai Shi WANG,Zhi Yuan HUANG.A Moment Characterization of B-Valued Generalized Functionals of White Noise[J].Acta Mathematica Sinica,English Series,2006,22(1):157-168. 被引量:4
  • 3王才士,陈金淑,屈明双.B-值白噪声广义泛函的解析刻画[J].数学物理学报(A辑),2007,27(2):322-330. 被引量:7
  • 4Obata, N, Wick product of white noise operators and its application to quantum stochastic differential equations, RIMS Kokyuroku, 957(1996): 167-185.
  • 5Chung, D.M., Chung, T.S. and Ji, U.C., A characterization theorem for operators on white noise functionals, Journal of the Mathematical Society of Japan, 51(2)(1999): 437-447.
  • 6Wang, C.S., Delta functions of observables and Radon - Nikodym derivatives of spectral measures, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 12(3)(2009): 427-437.
  • 7Han, Q., Wang, C.S. and Zhou, Y.L., Convolution of functionals of discrete-time normal martingales, Bulletin of the Australian Mathematical Society, 86(2)(2012): 224-231.
  • 8黄志远,王才士,让光林.量子白噪声分析,湖北科学技术出版社,2004.
  • 9Huang, Z.Y. and Yan, J.A., Introduction to Infinite Dimensional Stochastic Analysis, Dordrecht: Kluwer Academic, 1999.
  • 10Huang, Z.Y. and Luo, L.S., Wick calculus of generalized operators and its applications to quan- tum stochastic calculus, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 1(3)(1998): 455-466.

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