Existence and uniqueness of solutions to degenerate stochastic integro-differential equations are proved in Bessel potential spaces.
On solvability of integro-differential equations
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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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2019 1verdicts
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On $L_p$-Solvability of Stochastic Integro-Differential Equations
Existence and uniqueness of solutions to degenerate stochastic integro-differential equations are proved in Bessel potential spaces.