On Lp-solvability of stochastic integro-differential equations
In this thesis, we investigate the Lp-solvability of a class of (possibly) degenerate stochastic integro-differential equations (SIDEs) of parabolic type, which includes the Zakai equation in nonlinear filtering for jump diffusions and the Kolmogorov equations for jump diffusions. We first study the solvability of integro-differential equations in the same type but without randomness. Then we present an Itˆo formula for the Lp-norm of jump processes having stochastic differentials in Lp-spaces, which can be used to study the solvability of SIDEs. In the last chapter, existence and uniqueness of the solutions to SIDEs are established in Bessel potential spaces.