On Solvability of Integro-Differential Equations

Marta  de León-Contreras; Istvan Gyongy; Sizhou Wu

doi:10.1007/s11118-020-09864-2

On Solvability of Integro-Differential Equations

Marta de León-Contreras, Istvan Gyongy, Sizhou Wu

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces and in Sobolev-Slobodeckij spaces. Generalisations to stochastic integro-differential equations, arising in filtering theory of jump diffusions, will be given in a forthcoming paper.

Original language	English
Pages (from-to)	443-475
Journal	Potential analysis
Volume	55
Early online date	25 Aug 2020
DOIs	https://doi.org/10.1007/s11118-020-09864-2
Publication status	Published - 31 Oct 2021

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10.1007/s11118-020-09864-2

POTA-D-19-00141_R1Accepted author manuscript, 930 KB

https://arxiv.org/abs/1809.06840

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title = "On Solvability of Integro-Differential Equations",

abstract = "A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces and in Sobolev-Slobodeckij spaces. Generalisations to stochastic integro-differential equations, arising in filtering theory of jump diffusions, will be given in a forthcoming paper. ",

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AU - Gyongy, Istvan

AU - Wu, Sizhou

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N2 - A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces and in Sobolev-Slobodeckij spaces. Generalisations to stochastic integro-differential equations, arising in filtering theory of jump diffusions, will be given in a forthcoming paper.

AB - A class of (possibly) degenerate integro-differential equations of parabolic type is considered, which includes the Kolmogorov equations for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces and in Sobolev-Slobodeckij spaces. Generalisations to stochastic integro-differential equations, arising in filtering theory of jump diffusions, will be given in a forthcoming paper.

U2 - 10.1007/s11118-020-09864-2

DO - 10.1007/s11118-020-09864-2

M3 - Article

SN - 0926-2601

VL - 55

SP - 443

EP - 475

JO - Potential analysis

JF - Potential analysis

ER -

On Solvability of Integro-Differential Equations

Abstract

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