Journal of the Mathematical Society of Japan

An exercise in Malliavin's calculus

Daniel W. STROOCK

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Abstract

This note has two goals. First, for those who have heard the term but do not know what it means, it provides a gentle introduction to Malliavin's calculus as it applies to degenerate parabolic partial differential equations. Second, it applies that theory to generalizations of Kolmogorov's example of a highly degenerate operator which is nonetheless hypoelliptic.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 4 (2015), 1785-1799.

Dates
First available in Project Euclid: 27 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1445951167

Digital Object Identifier
doi:10.2969/jmsj/06741785

Mathematical Reviews number (MathSciNet)
MR3417514

Zentralblatt MATH identifier
1329.35121

Subjects
Primary: 35H10: Hypoelliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations 60J65: Brownian motion [See also 58J65]

Keywords
hypoelliptic equations

Citation

STROOCK, Daniel W. An exercise in Malliavin's calculus. J. Math. Soc. Japan 67 (2015), no. 4, 1785--1799. doi:10.2969/jmsj/06741785. https://projecteuclid.org/euclid.jmsj/1445951167


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References

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