A generalization of an extended stochastic integral

被引：0
作者：
Albeverio S. [1 ]
Berezansky Yu.M. [2 ]
Tesko V.A. [2 ]
机构：
[1] Institut für Angewandte Mathematik, Universität Bonn, Bonn
[2] Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv
来源：
Ukrainian Mathematical Journal | 2007年 / 59卷 / 5期
关键词：
Hilbert Space; Stochastic Integral; Complex Hilbert Space; Poisson Measure; Functional Realization;
D O I：
10.1007/s11253-007-0044-x
中图分类号：
学科分类号：
摘要：
We propose a generalization of an extended stochastic integral to the case of integration with respect to a broad class of random processes. In particular, we obtain conditions for the coincidence of the considered integral with the classical Itô stochastic integral. © 2007 Springer Science+Business Media, Inc.
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页码：645 / 677
页数：32
相关论文
共 56 条
[1]  
Hitsuda M., Formula for Brownian partial derivatives, Proceedings of the Second Japan-USSR Symposium on Probability Theory, 2, pp. 111-114, (1972)
[2]  
Daletsky Ju. L., Paramonova S.N., Stochastic integrals with respect to a normally distributed additive set function, Dokl. Akad. Nauk SSSR, 208, pp. 512-515, (1973)
[3]  
Daletsky Ju. L., Paramonova S.N., A formula of the theory of Gaussian measures and the estimation of stochastic integrals, Teor. Ver. Primen., 19, pp. 844-849, (1974)
[4]  
Skorokhod A.V., On the generalization of the stochastic integral, Teor. Ver. Primen., 20, pp. 223-228, (1975)
[5]  
Kabanov Yu.M., Skorokhod A.V., Extended stochastic integrals, Proceedings of the School and Seminar on the Theory of Random Processes [in Russian], Part 1, pp. 123-167, (1975)
[6]  
Kabanov Yu. M., Extended stochastic integrals, Teor. Ver. Primen., 20, pp. 725-737, (1975)
[7]  
Kachanovsky N.A., On the extended stochastic integral connected with the gamma-measure on an infinite-dimensional space, Meth. Funct. Anal. Topol., 8, pp. 10-32, (2002)
[8]  
Kachanovsky N.A., On the extended stochastic integral and Wick calculus on the spaces of regular generalized functions connected with the Gamma-measure, Ukr. Mat. Zh., 57, pp. 1030-1057, (2005)
[9]  
Hida T., Kuo H.-H., Potthoff J., Streit L., White Noise. An Infinite-Dimensional Calculus, (1993)
[10]  
Norin N.V., The Extended Stochastic Integral in Linear Spaces with Differentiable Measures and Related Topics, (1996)
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