COUPLING LÉVY MEASURES AND COMPARISON PRINCIPLES FOR VISCOSITY SOLUTIONS

Nestor GUILLEN; Chenchen MOU; Andrzej ŚWIĘCH

doi:10.1090/tran/7877

COUPLING LÉVY MEASURES AND COMPARISON PRINCIPLES FOR VISCOSITY SOLUTIONS

Nestor GUILLEN, Chenchen MOU, Andrzej ŚWIĘCH

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	7327-7370
Journal	Transactions of the American Mathematical Society
Volume	372
Issue number	10
Online published	28 Aug 2019
DOIs	https://doi.org/10.1090/tran/7877
Publication status	Published - 15 Nov 2019
Externally published	Yes

Research Keywords

Comparison principles
Lévy measures
Nonlocal equations
Optimal transport
Uniqueness
Viscosity solutions

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10.1090/tran/7877

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title = "COUPLING L{\'E}VY MEASURES AND COMPARISON PRINCIPLES FOR VISCOSITY SOLUTIONS",

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 L{\'e}vy-It{\^o} type. The main idea is to use an optimal transport map to couple two different L{\'e}vy measures and use the resulting coupling in a doubling of variables argument.",

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author = "Nestor GUILLEN and Chenchen MOU and Andrzej {\'S}WI{\c E}CH",

year = "2019",

month = nov,

day = "15",

doi = "10.1090/tran/7877",

language = "English",

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journal = "Transactions of the American Mathematical Society",

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AU - GUILLEN, Nestor

AU - MOU, Chenchen

AU - ŚWIĘCH, Andrzej

PY - 2019/11/15

Y1 - 2019/11/15

N2 - 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.

AB - 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.

KW - Comparison principles

KW - Lévy measures

KW - Nonlocal equations

KW - Optimal transport

KW - Uniqueness

KW - Viscosity solutions

KW - Comparison principles

KW - Lévy measures

KW - Nonlocal equations

KW - Optimal transport

KW - Uniqueness

KW - Viscosity solutions

KW - Comparison principles

KW - Lévy measures

KW - Nonlocal equations

KW - Optimal transport

KW - Uniqueness

KW - Viscosity solutions

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U2 - 10.1090/tran/7877

DO - 10.1090/tran/7877

M3 - RGC 21 - Publication in refereed journal

SN - 0002-9947

VL - 372

SP - 7327

EP - 7370

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 10

ER -

COUPLING LÉVY MEASURES AND COMPARISON PRINCIPLES FOR VISCOSITY SOLUTIONS

Abstract

Research Keywords

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