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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Analyse quasi-sure et l’estimation du noyau de la chaleur pour temps petit
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Trans. Amer. Math. Soc. 339 (1993), 221-241 Request permission


The Ito functional can be redefined out of a slim set by the natural way. Quasi-sure analysis is used to deal with the heat kernel asymptotic problems.
  • H. Airault and P. Malliavin, Intégration géométrique sur l’espace de Wiener, Bull. Sci. Math. (2) 112 (1988), no. 1, 3–52 (French, with English summary). MR 942797
  • R. Azencott, Grandes déviations et applications, Eighth Saint Flour Probability Summer School—1978 (Saint Flour, 1978), Lecture Notes in Math., vol. 774, Springer, Berlin, 1980, pp. 1–176 (French). MR 590626
  • —, Formule de Taylor stochastique et développements asymptotiques de Feynmann, Sém. Probabilité XVI, 1980-1981, Lecture Notes 921, pp. 237-284.
  • G. Ben Arous, Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 3, 307–331 (French). MR 974408, DOI 10.24033/asens.1560
  • Jean-Michel Bismut, Large deviations and the Malliavin calculus, Progress in Mathematics, vol. 45, Birkhäuser Boston, Inc., Boston, MA, 1984. MR 755001
  • —, Mécanique aléatoire, Lecture Notes in Math., vol. 866, Springer-Verlag, Berlin and New York, 1981.
  • Halim Doss, Démonstration probabiliste de certains développements asymptotiques quasi classiques, Bull. Sci. Math. (2) 109 (1985), no. 2, 179–208 (French, with English summary). MR 802532
  • Richard S. Ellis and Jay S. Rosen, Asymptotic analysis of Gaussian integrals. I. Isolated minimum points, Trans. Amer. Math. Soc. 273 (1982), no. 2, 447–481. MR 667156, DOI 10.1090/S0002-9947-1982-0667156-0
  • A. Erdélyi, Asymptotic expansions, Dover Publications, Inc., New York, 1956. MR 0078494
  • Shizan Fang, Le calcul différentiel quasi-sûr et son application à l’estimation du noyau de la chaleur, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 6, 369–372 (French, with English summary). MR 1071646
  • Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
  • Nobuyuki Ikeda and Shinzo Watanabe, Stochastic differential equations and diffusion processes, 2nd ed., North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. MR 1011252
  • Shigeo Kusuoka and Daniel Stroock, Applications of the Malliavin calculus. I, Stochastic analysis (Katata/Kyoto, 1982) North-Holland Math. Library, vol. 32, North-Holland, Amsterdam, 1984, pp. 271–306. MR 780762, DOI 10.1016/S0924-6509(08)70397-0
  • Rémi Léandre, Intégration dans la fibre associée à une diffusion dégénérée, Probab. Theory Related Fields 76 (1987), no. 3, 341–358 (French). MR 912659, DOI 10.1007/BF01297490
  • Paul Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976) Wiley, New York-Chichester-Brisbane, 1978, pp. 195–263. MR 536013
  • —, Implicit functions theorem in finite corank on the Wiener space, Taniguechi Sympos. SA-Katata 1982 (K. Ito, ed.), 1984, pp. 369-386. —, Differential analysis in stochastic analysis, Course at MIT, 1984. —, Géométrie différentielle stochastique, Presses Univ. Montréal, Montréal, 1978.
  • H. P. McKean Jr., Stochastic integrals, Probability and Mathematical Statistics, No. 5, Academic Press, New York-London, 1969. MR 0247684
  • J.-M. Moulinier, Théorème limite pour les équations différentielles stochastiques, Bull. Sci. Math. (2) 112 (1988), no. 2, 185–209 (French, with English summary). MR 967145
  • Daniel Ocone and Étienne Pardoux, A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations, Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), no. 1, 39–71 (English, with French summary). MR 995291
  • Jia Gang Ren, Analyse quasi-sûre des équations différentielles stochastiques, Bull. Sci. Math. 114 (1990), no. 2, 187–213 (French, with English summary). MR 1056161
  • D. W. Stroock, An introduction to the théory of large deviation, Springer, New York, 1988. D. W. Stroock et S. R. S. Varadhan, On the support on diffusion processes with applications to the strong maximum principle, Proc. 6th Berkeley Sympos. on Math. Stat. and Prob., vol. 3, Univ. of California Press, Berkeley, 1972, pp. 335-359.
  • Hiroshi Sugita, Positive generalized Wiener functions and potential theory over abstract Wiener spaces, Osaka J. Math. 25 (1988), no. 3, 665–696. MR 969026
  • S. Watanabe, Lectures on stochastic differential equations and Malliavin calculus, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 73, Published for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1984. Notes by M. Gopalan Nair and B. Rajeev. MR 742628
  • Shinzo Watanabe, Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels, Ann. Probab. 15 (1987), no. 1, 1–39. MR 877589
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 339 (1993), 221-241
  • MSC: Primary 60H30; Secondary 58G32, 60H07
  • DOI:
  • MathSciNet review: 1108611