Coupling by Change of Measure, Harnack Inequality and Hypercontractivity
The coupling method is a powerful tool in analysis of stochastic processes. To make the coupling successful before a given time, it is essential that two marginal processes are constructed under different probability measures. We explain the main idea of establishing Harnack inequalities for Markov semigroups using these new type couplings, and apply the coupling and Harnack inequality to the study of hypercontractivity of Markov semigroups.
KeywordsCoupling by change of measure Harnack inequality Hypercontractivity Degenerate SDEs
The author would like to thank the referee for helpful comments and a number of corrections. The work is supported by NNSFC (11771326, 11431014).
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