High Quality Content by WIKIPEDIA articles! In mathematics, the Ornstein–Uhlenbeck operator can be thought of as a generalization of the Laplace operator to an infinite-dimensional setting. The Ornstein–Uhlenbeck operator plays a significant role in the Malliavin calculus.Often, when working on Rn, one works with respect to Lebesgue measure, which has many nice properties. However, remember that the aim is to work in infinite-dimensional spaces, and it is a fact that there is no infinite-dimensional Lebesgue measure. Instead, if one is studying some separable Banach space E, what does make sense is a notion of Gaussian measure; in particular, the abstract Wiener space construction makes sense.

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