Second order stochastic inclusion. Part II.
by
Jerzy Motyl
Institute of Mathematics, University of Zielona Góra, Poland
Coauthors: Mariusz Michta (University of Zielona Góra, Poland)

Let F and H be set-valued functions, while Y and Z denote two arbitrary semimartingales. Under certain measurability conditions there exists a set-valued stochastic

integral ó õ ó õ FdYdZ defined as Aumann's type integral, i.e. the integral is meant as a set of integrals of suitable selectors. Given such integrals it is possible to define

stochastic inclusion as a relation of the form:

Xt in Ht+ ó õ t 0  [ ó õ s- 0  F(u , Xu -)dYu]dZs,       t, s in R+.

The problem of the existence of weak solutions to the above inclusion is considered. The result follows using set-valued analysis methods and can be applied to some stochastic control problems presented in Part I (by M. Michta).

Date received: October 28, 2002