On Lp-solvability of stochastic integro-differential equations
Abstract
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.