Set-valued stochastic integrals with respect to Poisson processes in a Banach space Original Research Article

In a separable Banach space image, at first we study image-valued stochastic integrals with respect to the Poisson random measure image and the compensated Poisson random measure image generated by a stationary Poisson stochastic process image. When the characteristic measure image of image is finite, both image and image are of finite variation a.s. Then the set-valued integrals with respect to the Poisson random measure and the compensated Poisson random measure are integrably bounded. The set-valued integral with respect to the compensated Poisson random measure is a right continuous (under Hausdorff metric) set-valued martingale.