Abstract
AbstractA 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.
Publisher
Springer Science and Business Media LLC
Reference43 articles.
1. Applebaum, D: Lévy processes and stochastic calculus. Cambridge University Press, Cambridge (2009)
2. Barndorff-Nielsen, O.E., Mikosch, T., Resnick, S.I. (eds.): Levy Processes. Theory and Applicationś. Birkhäuser, Cambridge (2001)
3. Bucur, C., Valdinoci, E.: Nonlocal diffusion and applications, lecture notes of the unione matematica italiana. Springer International Publishing, Switzerland (2016)
4. Caffarelli, L., Silvestre, L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 32(7-9), 1245–1260 (2007)
5. Caffarelli, L., Salsa, S., Silvestre, L.: Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Inventiones Math. 171(2), 425–461 (2008)
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1. On partially observed jump diffusions II: the filtering density;Stochastics and Partial Differential Equations: Analysis and Computations;2023-10-03