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), p. 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},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {327},
     year = {2009},
     pages = {93-114},
     zbl = {1201.60054},
     mrnumber = {2642354},
     language = {en},
     url = {http://www.numdam.org/item/AST_2009__327__93_0}
}
Norris, James R. Two-parameter stochastic calculus and Malliavin's integration-by-parts formula on Wiener space, in 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. | Article | MR 621660 | Zbl 0445.60049

[2] R. Cairoli & J. B. Walsh - "Stochastic integrals in the plane", Acta Math. 134 (1975), p. 111-183. | Article | MR 420845 | Zbl 0334.60026

[3] R. J. Elliott & M. Kohlmann - "Integration by parts, homogeneous chaos expansions and smooth densities", Ann. Probab. 17 (1989), p. 194-207. | Article | MR 972781 | Zbl 0671.60050

[4] K. D. Elworthy & X.-M. Li - "Formulae for the derivatives of heat semigroups", J. Funct Anal. 125 (1994), p. 252-286. | Article | MR 1297021 | Zbl 0813.60049

[5] R. Léandre - "The geometry of Brownian surfaces", Probab. Surv. 3 (2006), p. 37-88. | Article | MR 2216962 | Zbl 1189.60104

[6] P. Malliavin - "C k -hypoellipticity with degeneracy", in Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, III, 1978), Academic Press, 1978, p. 199-214. | MR 517243 | Zbl 0449.58022

[7] P. Malliavin, "C k -hypoellipticity with degeneracy. II", in Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, III., 1978), Academic Press, 1978, p. 327-340. | MR 517250 | Zbl 0449.58023

[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 536013 | Zbl 0411.60060

[9] J. R. Norris - "Twisted sheets", J. Funct. Anal. 132 (1995), p. 273-334. | Article | MR 1347353 | Zbl 0848.60055

[10] I. Shigekawa - "Derivatives of Wiener functionals and absolute continuity of induced measures", J. Math. Kyoto Univ. 20 (1980), p. 263-289. | Article | MR 582167 | Zbl 0476.28008

[11] D. W. Stroock - "The Malliavin calculus, a functional analytic approach", J. Funct. Anal. 44 (1981), p. 212-257. | Article | MR 642917 | Zbl 0475.60060

[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. | Article | MR 603973 | Zbl 0474.60061

[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. | Article | MR 616961 | Zbl 0474.60062

[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. | Article | MR 370758 | Zbl 0282.60030

[15] E. Wong & M. Zakai, "Differentiation formulas for stochastic integrals in the plane", Stochastic Processes Appl. 6 (1977/78), p. 339-349. | Article | MR 651571 | Zbl 0372.60078