Stochastic Integration in Abstract Spaces

[摘要] We establish the existence of a stochastic integral in a nuclear space settingas follows. LetE,F, andGbe nuclear spaces which satisfy the followingconditions: the spaces are reflexive, complete, bornological spaces such that theirstrong duals also satisfy these conditions. Assume that there is a continuousbilinear mapping ofE×FintoG. IfHis an integrable,E-valued predictableprocess andXis anF-valued square integrable martingale, then there exists aG-valued process(∫HdX)tcalled the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.

[学科分类] 应用数学