A Representation for Some Martingales

Previous article Next article A Representation for Some MartingalesL. I. Gal’chukL. I. Gal’chukhttps://doi.org/10.1137/1121071PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. D. Ventcel', Additive functionals on a multi-dimensional Wiener process, Dokl. Akad. Nauk SSSR, 139 (1961), 13–16, (In Russian.) MR0139201 (25:2637) Google Scholar[2] Hiroshi Kunita and , Shinzo Watanabe, On square integrable martingales, Nagoya Math. J., 30 (1967), 209–245 MR0217856 (36:945) 0167.46602 CrossrefGoogle Scholar[3] J. M. C. Clark, The representation of functionals of Brownian motion by stochastic integrals, Ann. Math. Statist., 41 (1970), 1282–1295 MR0270448 (42:5336) 0213.19402 CrossrefGoogle Scholar[4] Yu. M. Kabanov, Representation of functionals of a Wiener and of Poisson processes in the form of stochastic integrals., Theory Prob. Applications, 18 (1973), 376–380 0316.60039 Google Scholar[5] R. Sh. Liptser and , A. N. Shiryaev, Statistics of random processes, Nauka, Moscow, 1974, (In Russian.) Google Scholar[6] B. Maisonneuve, Quelques martingales remarquables associées à une martingale continue, Publ. Inst. Statist. Univ. Paris, 17 (1968), 13–27 MR0283868 (44:1098) 0196.19201 Google Scholar[7] Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1966xiii+266 MR0205288 (34:5119) 0138.10401 Google Scholar[8] C. Doléans-Dade and , P.-A. Meyer, Intégrales stochastiques par rapport aux martingales locales, Séminaire de Probabilités, IV (Univ. Strasbourg, 1968/69), Lecture Notes in Mathematics, Vol. 124. Springer, Berlin, 1970, 77–107 MR0270425 (42:5313) 0211.21901 Google Scholar[9] N. N. Luzin, Leçons sur les ensembles analytiques et leurs applications, Gautheir-Villars, Paris, 1930 0009.05505 Google Scholar[10] Nelson Dunford and , Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York, 1958xiv+858 MR0117523 (22:8302) 0084.10402 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails The Predictable Representation Property of Compensated-Covariation Stable Families of MartingalesP. Di Tella and H.-J. Engelbert3 March 2016 | Theory of Probability & Its Applications, Vol. 60, No. 1AbstractPDF (350 KB)Stochastic Integral Representation of Functionals from a Sequence of Martingales Cross Ref Stable Subspaces and a Decomposition Theorem for MartingalesL. I. Gal’chuk17 July 2006 | Theory of Probability & Its Applications, Vol. 25, No. 2AbstractPDF (467 KB)Existence and Uniqueness of a Solution for Stochastic Equations with Respect to SemimartingalesL. I. Gal’chuk17 July 2006 | Theory of Probability & Its Applications, Vol. 23, No. 4AbstractPDF (1146 KB)A Generalization of Girsanov’s Theorem on Substitution of Measures to the Case of Semi-Martingales with JumpsL. I. Gal’chuk17 July 2006 | Theory of Probability & Its Applications, Vol. 22, No. 2AbstractPDF (1242 KB) Volume 21, Issue 3| 1977Theory of Probability & Its Applications History Submitted:25 September 1975Published online:28 July 2006 InformationCopyright © 1977 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1121071Article page range:pp. 599-605ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics