  In an M-type 2 Banach space, firstly we explore some properties of the
set-valued stochastic integral associated with the stationary Poisson point
process. By using the Hahn decomposition theorem and bounded linear functional,
we obtain the main result: the integral of a set-valued stochastic process with
respect to the compensated Poisson measure is a set-valued submartingale but
not a martingale unless the integrand degenerates into a single-valued process.
Secondly we study the strong solution to the set-valued stochastic integral
equation, which includes a set-valued drift, a single-valued diffusion driven
by a Brownian motion and the set-valued jump driven by a Poisson process.
