Abstract
The Malliavin calculus (also known as the stochastic calculus of variations) is an infinite-dimensional differential calculus on the Wiener space. It is tailored to investigate regularity properties of the law of Wiener functionals such as solutions of stochastic differential equations. This theory was initiated by Malliavin and further developed by Stroock, Bismut, Watanabe, and others. The original motivation, and the most important application of this theory, has been to provide a probabilistic proof of Hörmander’s “sum of squares” theorem.
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© 1995 Springer Science+Business Media New York
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Nualart, D. (1995). Introduction. In: The Malliavin Calculus and Related Topics. Probability and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2437-0_1
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DOI: https://doi.org/10.1007/978-1-4757-2437-0_1
Publisher Name: Springer, New York, NY
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