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Coupling by Change of Measure, Harnack Inequality and Hypercontractivity

  • Feng-Yu WangEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

Abstract

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.

Keywords

Coupling by change of measure Harnack inequality Hypercontractivity Degenerate SDEs 

Notes

Acknowledgements

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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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Applied MathematicsTianjin UniversityTianjinChina

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