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Zap. Nauchn. Sem. POMI, 1999, Volume 260, Pages 164–185 (Mi znsl1072)  

This article is cited in 3 scientific papers (total in 3 papers)

An expansion of multilpe Stratonovich stochastic integrals, based on multiple Fourier expansion

D. F. Kuznetsov

Saint-Petersburg State Polytechnical University

Abstract: The expansion of multiple Stratonovich stochastic integrals of multiplicity $k$; $k\in N$ into multiple series of products of Gaussian random values is stated and proved. The coefficients of this expansion are the coefficients of multiple Fourier expansion of the function of several variables on full orthonormal systems in space $L_2([t,T])$. For expansion the convergence in mean of order $n$; $n\in N$ is proved. Some expansions of multiple Stratonovich stochastic integrals with the help of polynomial and trigonometric systems are considered.

Full text: PDF file (268 kB)

English version:
Journal of Mathematical Sciences (New York), 2002, 109:6, 2148–2165

Bibliographic databases:

UDC: 519.2
Received: 11.02.1999

Citation: D. F. Kuznetsov, “An expansion of multilpe Stratonovich stochastic integrals, based on multiple Fourier expansion”, Probability and statistics. Part 3, Zap. Nauchn. Sem. POMI, 260, POMI, St. Petersburg, 1999, 164–185; J. Math. Sci. (New York), 109:6 (2002), 2148–2165

Citation in format AMSBIB
\Bibitem{Kuz99}
\by D.~F.~Kuznetsov
\paper An expansion of multilpe Stratonovich stochastic integrals, based on multiple Fourier expansion
\inbook Probability and statistics. Part~3
\serial Zap. Nauchn. Sem. POMI
\yr 1999
\vol 260
\pages 164--185
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1072}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1759161}
\zmath{https://zbmath.org/?q=an:1001.60063}
\transl
\jour J. Math. Sci. (New York)
\yr 2002
\vol 109
\issue 6
\pages 2148--2165
\crossref{https://doi.org/10.1023/A:1014581416903}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. F. Kuznetsov, “New representations of explicit one-step numerical methods for jump-diffusion stochastic differential equations”, Comput. Math. Math. Phys., 41:6 (2001), 874–888  mathnet  mathscinet  zmath
    2. Espinosa L.A.D., Gray W.S., Gonzalez O.R., “Growth Bounds for Iterated Integrals of L-2-Ito Random Processes”, SSST: 2009 41st Southeastern Symposium on System Theory, Southeastern Symposium on System Theory, 2009, 223–229  isi
    3. Espinosa L.A.D., Gray W.S., Gonzalez O.R., “On the Absolute Global Convergence of Fliess Operators Driven by L-2-Ito Processes”, 2010 42nd Southeastern Symposium on System Theory (SSST), Southeastern Symposium on System Theory, 2010  isi
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