On L_p-Solvability of Stochastic Integro-Differential Equations

2019/07/10 by Gyöngy, István, Wu, Sizhou
#35B65 (Secondary) #45K05 #60H15 #60H20 #60J75 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1907.04876

Abstract

A class of (possibly) degenerate stochastic integro-differential equations of parabolic type is considered, which includes the Zakai equation in nonlinear filtering for jump diffusions. Existence and uniqueness of the solutions are established in Bessel potential spaces.

Related

• On solvability of integro-differential equations
• Model problem for integro-differential Zakai equation with discontinuous observation processes in Hölder spaces
• A Note On Degenerate Stochastic Integro-Differential Equations
• Degenerate Irregular SDEs with Jumps and Application to Integro-Differential Equations of Fokker-Planck type
• On Degenerate Linear Stochastic Evolution Equations Driven by Jump Processes