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 |
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Pages (from-to) | 443-475 |
Journal | Potential analysis |
Volume | 55 |
Early online date | 25 Aug 2020 |
DOIs | |
Publication status | Published - 31 Oct 2021 |