Stochastic integrals and differential systems

摘要: We abstract and extend the stochastic integration with martingale integrators to more general processes for which dominated convergence theorem is still valid. The motivation here obtain a unified treatment of several different integrals, available in literature, by means generalized boundedness principle based on fundamental idea formulated S. Bochner. After presenting semi-martingale integrals next section, serve as key example, desired treated detail Section 2. It also shown there, 3, that earlier fit this frame work; applications are worked out exhibit universality principle, including some vector multiparameter cases. rest chapter devoted existence (and unicity) solutions both linear nonlinear higher order differential equations its progression flows L 2,2-bounded case. This work takes up Sections 4 5 below, most appears book form first time. Several other results included Complements section.