Abstract
In a separable Banach space \(\mathfrak{X}\), after studying \(\mathfrak{X}\)-valued stochastic integrals with respect to Poisson random measure N(dsdz) and the compensated Poisson random measure N (dsdz) generated by stationary Poisson stochastic process P, we prove that if the characteristic measure ν of P is finite, the stochastic integrals (denoted by {J t (F)} and {I t (F)} separately) for set-valued stochastic process {F(t)} are integrably bounded and convex a.s. Furthermore, the set-valued integral {I t (F)} with respect to compensated Poisson random measure is a right continuous (under Hausdorff metric) setvalued martingale.
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