**Publications **

A quasi-invariance theorem for measures on Banach spaces *Trans. Amer. Math. Soc.* **290** (1985) 851-855.

On the relationship between differentiability and absolute continuity of measures on **R**^{n}*.* *Prob. Theor. Rel. Fields*. **72** (1986) 417-424.

On the equivalence of absolute continuity and quasi-translation invariance for Borel measures on an LCA group*. Math. Proc. Cam. Phil. Soc. ***101** (1987) 279-281.

*The Malliavin Calculus. *Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 34 *.* Longman, Essex; Wiley, NY, 1987.

On the solution of stochastic differential equations via small delays (with S. Mohammed)*.* *Stochastics ***28** (1989) 293-299.

Transformations of measure on infinite-dimensional vector space*.* *Seminar on Stochastic Processes, 1990, * 15-25*.* Birkhäuser, Boston, 1991.

The Malliavin calculus and stochastic delay equations (with S. Mohammed)*.* *J. Funct. Anal. ***99** (1991) 75-99.

A calcium model with random absorption: a stochastic approach (with P. Sen and D. Mohr)*.* *J. Theor. Biol. ***154** (1992) 485-493.

On the limitations of a well-known integration technique*.* *Math. Mag.* **66** (1993) 243-244.

Hypoelliptic parabolic operators with exponential degeneracies (with S. Mohammed)*.* * C. R. Acad. Sci. Paris ***317** (1993) 1059-1064.

Degenerate stochastic differential equations, flows, and hypoellipticity (with S. Mohammed). *Proc. Symposia Pure Math.*** 57**, 553-564

An extension of Hormander's theorem for infinitely degenerate second-order operators (with S. Mohammed)*.* *Duke Math J. ***78**, no. 3 (1995) 453-475.

Smooth densities for degenerate stochastic differential equations with hereditary drift (with S. Mohammed)*.* *Ann. Prob.* **23**, no. 4 (1995) 1875-1894.

*Degenerate Stochastic Differential Equations and Hypoellipticity. *Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 79. Longman, Essex, 1995.

The Dirichlet problem for superdegenerate differential operators (with S. Mohammed)*.* *C. R. Acad. Sci. Paris ***327** (1998) 81-86.

Review of *Stochastic Analysis* by Paul Malliavin*.* *Ann. Prob*. **30**, no. 1 (2002) 474-479.

Stochastic differential equations and hypoelliptic operators*.* *Real and Stochastic Analysis*, 9 - 42, Trends. Math., Birkhauser, Boston MA, 2004.

Divergence theorems in path space*.* *J. Funct. Anal. ***218**, no. 1 (2005) 130-149.

A model for the interaction of two chemicals (with P. Sen). *J. Theor. Biol.* **238** (2006), 652-656.

Divergence theorems in path space II: degenerate diffusions. *C. R. Acad. Sci. Paris,* *Ser. I* **342** (2006) 869-872.

*The Malliavin Calculus*, 2nd edition*.* Dover Publishing, Mineola, NY, 2006. With new appendix: Admissible vector fields and quasi-invariant measures.

*Quasi-invariant measures on the path space of a diffusion**. C. R. Acad. Sci. Paris, Ser. I **343** (2006) 197-200.*

*The Gauss-Bonnet theorem for vector bundles**. J. Geom.** 85** no. 1-2 (2006) 15-21.*

*Divergence theorems in path space III: hypoelliptic diffusions and beyond**. J. Funct. Anal. **252**, no. 1 (2007) 232-253.*

Arbitrage-free option pricing models, *J. Aust. Math. Soc.* **87** (2009) 145-152.

Poisson's remarkable calculation - a method or a trick? *Elem. Math. **65** (2010) *1-8.

Associative binary operations and the Pythagorean Theorem. *Math. Intelligencer* **33**, no. 1 (2011) 92-95.

The Malliavin Calculus and Hypoelliptic Differential Operators.* Infinite Dimensional Analysis, Quantum Probability and Related Topics* **18**, no. 1 (2015), 24 pp.

Superdegenerate Hypoelliptic Differential Operators.* Probability on algebraic and geometric structures*, 13-20, *Contemp. Math., 668, Amer. Math. Soc., Providence, RI, *2016.

Noncentral limit theorem for the generalized Hermite process (with D. Nualart)*. Elec. Commun. Probab. ***22** (2017), no. 66, 1-13.