Quasi-invariance for families of infinite-dimensional SDEs with degenerate noise
Date
2022-08
Authors
Kim, Hyoungji
Major Professor
Advisor
Herzog, David P
Raúl Stinga, Pablo
Wu, Ruoyu
Yan, Jue
Yu, Cindy
Committee Member
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Abstract
We introduce quantitative functional inequalities for specific classes of hypoelliptic stochastic
differential equations (SDEs). In particular, these inequalities include the reverse logarithmic Sobolev
inequality and Wang-type Harnack inequality for a large class of linear SDEs with degenerate
noise. The inequalities are obtained from gradient bounds of the semigroup of the process and by
making use of the generalized version of the carre du champ operator. From these results, we
obtain quasi-invariance of the same form of SDEs that take values in an infinite-dimensional
Hilbert space, deducing a form of hypoellipticity in infinite dimensions.
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dissertation