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 Ñ (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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Zhang, J., Mitoma, I. (2011). Set-Valued Stochastic Integrals with Respect to Poisson Processes in a Banach Space. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_15
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DOI: https://doi.org/10.1007/978-3-642-22833-9_15
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