Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space
From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 93-114.
@incollection{AST_2009__327__93_0,
     author = {Norris, James R.},
     title = {Two-parameter stochastic calculus and {Malliavin's} integration-by-parts formula on {Wiener} space},
     booktitle = {From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut},
     editor = {Dai Xianzhe and L\'eandre R\'emi and Xiaonan Ma and Zhang Weiping},
     series = {Ast\'erisque},
     pages = {93--114},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     year = {2009},
     mrnumber = {2642354},
     zbl = {1201.60054},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__327__93_0/}
}
TY  - CHAP
AU  - Norris, James R.
TI  - Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space
BT  - From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut
AU  - Collectif
ED  - Dai Xianzhe
ED  - Léandre Rémi
ED  - Xiaonan Ma
ED  - Zhang Weiping
T3  - Astérisque
PY  - 2009
SP  - 93
EP  - 114
IS  - 327
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2009__327__93_0/
LA  - en
ID  - AST_2009__327__93_0
ER  - 
%0 Book Section
%A Norris, James R.
%T Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space
%B From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut
%A Collectif
%E Dai Xianzhe
%E Léandre Rémi
%E Xiaonan Ma
%E Zhang Weiping
%S Astérisque
%D 2009
%P 93-114
%N 327
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2009__327__93_0/
%G en
%F AST_2009__327__93_0
Norris, James R. Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space, dans From probability to geometry (I) - Volume in honor of the 60th birthday of Jean-Michel Bismut, Astérisque, no. 327 (2009), pp. 93-114. http://www.numdam.org/item/AST_2009__327__93_0/

[1] J.-M. Bismut - "Martingales, the Malliavin calculus and hypoellipticity under general Hörmander's conditions", Z. Wahrsch. Verw. Gebiete 56 (1981), p. 469-505. | DOI | MR | Zbl

[2] R. Cairoli & J. B. Walsh - "Stochastic integrals in the plane", Acta Math. 134 (1975), p. 111-183. | DOI | MR | Zbl

[3] R. J. Elliott & M. Kohlmann - "Integration by parts, homogeneous chaos expansions and smooth densities", Ann. Probab. 17 (1989), p. 194-207. | DOI | MR | Zbl

[4] K. D. Elworthy & X.-M. Li - "Formulae for the derivatives of heat semigroups", J. Funct Anal. 125 (1994), p. 252-286. | DOI | MR | Zbl

[5] R. Léandre - "The geometry of Brownian surfaces", Probab. Surv. 3 (2006), p. 37-88. | DOI | EuDML | MR | Zbl

[6] P. Malliavin - "Ck-hypoellipticity with degeneracy", in Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, III, 1978), Academic Press, 1978, p. 199-214. | MR | Zbl

[7] P. Malliavin, "Ck-hypoellipticity with degeneracy. II", in Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, III., 1978), Academic Press, 1978, p. 327-340. | MR | Zbl

[8] P. Malliavin, "Stochastic calculus of variation and hypoelliptic operators", in Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976), Wiley, 1978, p. 195-263. | MR | Zbl

[9] J. R. Norris - "Twisted sheets", J. Funct. Anal. 132 (1995), p. 273-334. | DOI | MR | Zbl

[10] I. Shigekawa - "Derivatives of Wiener functionals and absolute continuity of induced measures", J. Math. Kyoto Univ. 20 (1980), p. 263-289. | DOI | MR | Zbl

[11] D. W. Stroock - "The Malliavin calculus, a functional analytic approach", J. Funct. Anal. 44 (1981), p. 212-257. | DOI | MR | Zbl

[12] D. W. Stroock, "The Malliavin calculus and its application to second order parabolic differential equations. I", Math. Systems Theory 14 (1981), p. 25-65. | DOI | MR | Zbl

[13] D. W. Stroock, "The Malliavin calculus and its application to second order parabolic differential equations. II", Math. Systems Theory 14 (1981), p. 141-171. | DOI | MR | Zbl

[14] E. Wong & M. Zakai - "Martingales and stochastic integrals for processes with a multi-dimensional parameter", Z. Wahrsch. Verw. Gebiete 29 (1974), p. 109-122. | DOI | MR | Zbl

[15] E. Wong & M. Zakai, "Differentiation formulas for stochastic integrals in the plane", Stochastic Processes Appl. 6 (1977/78), p. 339-349. | DOI | MR | Zbl