Stochastic Integrals and Processes with Independent Increments

摘要

Stochastic integrals are defined using processes with independent increments as integrators. A simple and perhaps new method is given for obtaining approximating simple integrands. In the special case where the integrand is a stable motion of index p epsilon the integrand may have paths in Lp. Basic properties are established. Then the characteristic functions of integrals involving nonrandom integrands are computed and used to establish necessary and sufficient conditions for the independence of such integrals. (Author)