Gyongy, Istvan

Sabanis, Sotirios

Wu, Sizhou

other

2021-11-05T10:41:38Z

2021-11-05T10:41:38Z

2021-07-31

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.

https://hdl.handle.net/1842/38205

http://dx.doi.org/10.7488/era/1471

en

The University of Edinburgh

M. De Le´on-Contreras, I. Gy¨ongy and S. Wu, On solvability of integro-differential equations, Potential Anal (2020). https://doi.org/10.1007/s11118-020-09864-2

I. Gy¨ongy and S. Wu, Itˆo’s formula for jump processes in Lp-spaces, Stochastic processes and their applications, January 2021, Volume 131, pp. 523-552.

I. Gy¨ongy, S. Wu, On Lp-solvability of stochastic integro-differential equations, Stoch PDE: Anal Comp (2020). https://doi.org/10.1007/s40072-019-00160-8

stochastic partial differential equations

Ito formulas

integro-differential equations

On Lp-solvability of stochastic integro-differential equations

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy