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首页> 外文期刊>Journal of the Mathematical Society of Japan >Stochastic integrals and Brownian motion on abstract nilpotent Lie groups
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Stochastic integrals and Brownian motion on abstract nilpotent Lie groups

机译：Stochastic integrals and Brownian motion on abstract nilpotent Lie groups

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摘要

We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition of Brownian motions on a general class of infinite-dimensional nilpotent Lie groups based on abstract Wiener spaces. We then prove that a Cameron Martin type quasi-invariance result holds for the associated heat kernel measures in the non-degenerate case, and give estimates on the associated Radon Nikodym derivative. We also prove that a log Sobolev estimate holds in this setting.

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