The Fourier Transform of Wiener Functionals and Various Methods of Stochastic Integration

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Previous article Next article The Fourier Transform of Wiener Functionals and Various Methods of Stochastic IntegrationA. A. DorogovtsevA. A. Dorogovtsevhttps://doi.org/10.1137/1134088PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. V. Skorokhod, On a generalization of a stochastic integral, Theory Probab. Appl., 20 (1975), 219–233 10.1137/1120030 0333.60060 LinkGoogle Scholar[2] Shigeyoshi Ogawa and , Takeshi Sekiguchi, On the Itô formula of noncausal type, Proc. Japan Acad. Ser. A Math. Sci., 60 (1984), 249–251 86j:60133 0563.60051 CrossrefGoogle Scholar[3] V. Matskyavichyus, Symmetric stochastic integral equations of Fredholm type, Litovsk. Mat. Sb., 24 (1984), 121–130, (In Russian.) 87b:60080 0598.60065 Google Scholar[4] David Nualart and , Moshe Zakai, Generalized stochastic integrals and the Malliavin calculus, Probab. Theory Relat. Fields, 73 (1986), 255–280 88h:60110 0601.60053 CrossrefGoogle Scholar[5] A. V. Skorokhod, Random linear operators, Mathematics and its Applications (Soviet Series), D. Reidel Publishing Co., Dordrecht, 1984xvi+199, Boston 85a:60070 CrossrefGoogle Scholar[6] I. I. Gikhman and , A. V. Skorokhod, The theory of stochastic processes. I, Springer-Verlag, New York, 1974viii+570 49:11603 CrossrefGoogle Scholar[7] A. A. Dorogovtsev, On application of a Gaussian strong random operator to random elements, Theory Probab. Appl., 31 (1986), 717–719 10.1137/1131100 0658.60081 LinkGoogle Scholar[8] T. Hida, Analysis of Brownian Functionals, Carleton Math. Lect. Notes 13, 1978 Google Scholar[9] Yu. L. Daletskii and , S. V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces, Nauka, Moscow, 1983, (In Russian.) Google Scholar[10] N. N. Vakhania, , V. I. Tarieladze and , S. A. Chobanyan, Probability distributions on Banach spaces, Mathematics and its Applications (Soviet Series), Vol. 14, D. Reidel Publishing Co., Dordrecht, 1987xxvi+482 97k:60007 0698.60003 CrossrefGoogle Scholar[11] Hui-Hsiung Kuo, On Fourier transform of generalized Brownian functionals, J. Multivariate Anal., 12 (1982), 415–431 10.1016/0047-259X(82)90075-6 84d:60099 0491.60039 CrossrefGoogle Scholar[12] Y. Shiota and , T. Sekiguchi, $L\sp 2$-theory of noncausal stochastic integrals, Math. Rep. Toyama Univ., 8 (1985), 119–195 87j:60084 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Elements of a non-gaussian analysis on the spaces of functions of infinitely many variablesUkrainian Mathematical Journal, Vol. 62, No. 9 | 24 March 2011 Cross Ref Volume 34, Issue 4| 1990Theory of Probability & Its Applications565-752 History Submitted:29 June 1987Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1134088Article page range:pp. 705-709ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics