On Solvability of Integro-Differential Equations
Marta De León-Contreras, István Gyöngy, Sizhou Wu · Potential Analysis · 2020
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.