On solvability of integro-differential equations

2018/09/18 by De León-Contreras, Marta, Gyöngy, István, Wu, Sizhou
#35R09 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 45K05 #Secondary 47G20

paper · doi:10.48550/arxiv.1809.06840

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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