Coupling Lévy measures and comparison principles for viscosity solutions

Guillen, Nestor; Mou, Chenchen; Świȩch, Andrzej

doi:10.1090/tran/7877

Coupling Lévy measures and comparison principles for viscosity solutions
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by Nestor Guillen, Chenchen Mou and Andrzej Świȩch PDF

Trans. Amer. Math. Soc. 372 (2019), 7327-7370 Request permission

Abstract:

We prove new comparison principles for viscosity solutions of nonlinear integro-differential equations. The operators to which the method applies include but are not limited to those of Lévy–Itô type. The main idea is to use an optimal transport map to couple two different Lévy measures and use the resulting coupling in a doubling of variables argument.

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