Multiple stochastic integrals constructed by special expansions of products of the integrating stochastic processes

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• 作者：I. S. Borisov ; S. E. Khrushchev
• 关键词：multiple stochastic integral ; multiple Wiener–Itô integral ; orthogonal series ; expansion of stochastic process ; Hu–Meyer formula
• 刊名：Siberian Advances in Mathematics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：26
• 期：1
• 页码：1-16
• 全文大小：650 KB
• 参考文献：1.I. S. Borisov and A. A. Bystrov, “Constructing a stochastic integral of a nonrandom function without the orthogonality condition for the integrating measure,” Teor. Veroyatn. Primen. 50, 52 (2005) [Theory Probab. Appl. 50, 53 (2006)].MathSciNet CrossRef
  2.I. S. Borisov and A. A. Bystrov, “Limit theorems for canonical von Mises’ statistics based on dependent observations,” Sib. Matem. Zhur. 47, 1205 (2006) [Siberian Math. J. 47, 980 (2006)].MathSciNet MATH
  3.I. S. Borisov and S. E. Khrushchev, “Construcring multiple stochastic integrals with non-Gaussian productmeasures,” Siberian Adv. Math. 24, 75 (2014).CrossRef
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  7.A. Dasgupta and G. Kallianpur, “Multiple fractional integrals,” Probab. Theory Related Fields 115, 505 (1999)MathSciNet CrossRef MATH
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  13.P. Major, Multiple Wiener–ItôIntegrals, Lecture Notes inMath. 849, Berlin, Springer, 1981.
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• 作者单位：I. S. Borisov (1) (2)
  S. E. Khrushchev (2)
  
  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
  2. Novosibirsk State University, Novosibirsk, 630090, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Allerton Press, Inc. distributed exclusively by Springer Science+Business Media LLC
• ISSN：1934-8126

文摘

The paper deals with problems of constructing multiple stochastic integrals in the case when the product of increments of the integrating stochastic process admits an expansion as a finite sum of series with random coefficients. This expansion was obtained for a sufficiently wide class including centered Gaussian processes. In the paper, some necessary and sufficient conditions are obtained for the existence of multiple stochastic integrals defined by an expansion of the product of Wiener processes. It was obtained a recurrent representation for the Wiener stochastic integral as an analog of the Hu–Meyer formula.