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Abstract |
An explicit sufficient condition on the hypercontractivity is derived for the Markov semigroup associated to a class of functional stochastic differential equations. Consequently, the semigroup converges exponentially to its unique invariant probability measure in both L^2 and the totally variational norm, and it is compact in L^2 for large t. This provides a natural class of non-symmetric Markov semigroups which are compact for large time but non-compact for small time. A semi-linear model which may not satisfy this sufficient condition is also investigated. |
