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Analyse quasi-sure et l'estimation du noyau de la chaleur pour temps petit


Author: Shizan Fang
Journal: Trans. Amer. Math. Soc. 339 (1993), 221-241
MSC: Primary 60H30; Secondary 58G32, 60H07
DOI: https://doi.org/10.1090/S0002-9947-1993-1108611-6
MathSciNet review: 1108611
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Abstract: 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.


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  • [A-M] H. Airault et P. Malliavin, Intégration géométrique sur l'espace de Wiener, Bull. Sci. Math (2) 112 (1988), 3-52. MR 942797 (89f:60072)
  • [AZ$ _{1}$] R. Azencott, Grandes déviations et applications, Ecole d'été de Saint-Flour VIII, Lecture Notes 774, 1980. MR 590626 (81m:58085)
  • [AZ$ _{2}$] -, Formule de Taylor stochastique et développements asymptotiques de Feynmann, Sém. Probabilité XVI, 1980-1981, Lecture Notes 921, pp. 237-284.
  • [BE] G. Ben Arous, Développements asmptotiques du noyau de la chaleur hypoelliptique hors du cut-locus, Ann. Ecole Norm. Sup. 21 (1988), 307-331. MR 974408 (89k:60087)
  • [BI$ _{1}$] J. M. Bismut, Large deviation and Malliavin calculus, Progr. Math., no. 45, Birkhäuser, Basel, 1984. MR 755001 (86f:58150)
  • [BI$ _{2}$] -, Mécanique aléatoire, Lecture Notes in Math., vol. 866, Springer-Verlag, Berlin and New York, 1981.
  • [DO] H. Doss, Démonstration probabiliste de certains développements asymptotiques quasi classiques, Bull. Sci. Math. (2) 109 (1985), 179-208. MR 802532 (87g:60053)
  • [E-R] R. S. Ellis et J. S. Rosen, Asymptotic analysis of Gaussian integrals. I. Isolated minimum points, Trans. Amer. Math. Soc. 273, (1982), 447-481. MR 667156 (84h:60074a)
  • [ER] A. Erdelyi, Asymptotics expansions, Dover, New York, 1956. MR 0078494 (17:1202c)
  • [FA] S. Fang, Le calcul différentiel quasi-sûr et son application à l'estimation du noyau de la chaleur, C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), 369-372. MR 1071646 (91f:60109)
  • [HO] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1969), 147-171. MR 0222474 (36:5526)
  • [I-W] N. Ikeda et S. Watanabe, Stochastic differential equations and diffusions processes, North-Holland, Amsterdam, 1981. MR 1011252 (90m:60069)
  • [K-S] S. Kusuoka et D. W. Stroock, Applications of the Malliavin calculus. II, J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 32 (1985), 1-76. MR 783181 (86k:60100b)
  • [LE] R. Leandre, Intégration dans la fibre associée à une diffusion dégénérée, Probab. Theory Related Fields 76 (1987), 341-358. MR 912659 (89g:60247)
  • [MA$ _{1}$] P. Malliavin, Stochastic calculus of variation and hypoeliptic operators, Proc. Int. Sympos. Stochastic Differential Equations, Kyoto, 1976 (K. Ito, ed.), Kinokuniya, 1978, pp. 195-263. MR 536013 (81f:60083)
  • [MA$ _{2}$] -, Implicit functions theorem in finite corank on the Wiener space, Taniguechi Sympos. SA-Katata 1982 (K. Ito, ed.), 1984, pp. 369-386.
  • [MA$ _{3}$] -, Differential analysis in stochastic analysis, Course at MIT, 1984.
  • [MA$ _{4}$] -, Géométrie différentielle stochastique, Presses Univ. Montréal, Montréal, 1978.
  • [Mc] H. P. McKean, Stochastic integrals, Academic Press, 1969. MR 0247684 (40:947)
  • [MO] J. M. Moulinier, Théorème limite pour les équations différentielles stochastiques, Bull. Sci. Math. (2) 112 (1988), 185-208. MR 967145 (89m:60138)
  • [O-P] D. Ocone et E. Pardoux, A generalized Itô-Ventzell formula. Application to a class of anticipating stochastic differential equations, Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), 39-71. MR 995291 (90g:60055)
  • [RE] J. Ren, Analyse stochatique quasi-sûre des équations différentielles stochastiques, Bull. Sci. Math. (2) 114, 90, 187-213. MR 1056161 (91m:60102)
  • [ST] D. W. Stroock, An introduction to the théory of large deviation, Springer, New York, 1988.
  • [S-V] D. W. Stroock et S. R. S. Varadhan, On the support on diffusion processes with applications to the strong maximum principle, Proc. 6th Berkeley Sympos. on Math. Stat. and Prob., vol. 3, Univ. of California Press, Berkeley, 1972, pp. 335-359.
  • [SU] H. Sugita, Positive generalized Wiener functions and potential theory over abstract Wiener spaces, Osaka J. Math. 25 (1988), 665-696. MR 969026 (90c:60036)
  • [WA$ _{1}$] S. Watanabe, Lectures on stochastic differential equations and Malliavin calculus, Tata Institute of Fundamental Research, Bombay, 1984. MR 742628 (86b:60113)
  • [WA$ _{2}$] -, Analysis of Wiener functionals (Malliavin calculus) and applications to heat kernels, Ann. Probab. 15 (1987), 1-39. MR 877589 (88h:60111)

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DOI: https://doi.org/10.1090/S0002-9947-1993-1108611-6
Article copyright: © Copyright 1993 American Mathematical Society

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