A Fubini Theorem for Iterated Stochastic Integrals.

摘要

This report extends the stochastic integral of Ito to allow for a certain class of anticipating integrals. Probabilistic and computational results concerning this extension are presented and iterated integrals are discussed. The motivation for this extension stems from the Ito-Volterra equation. This equation arises from feedback in the presence of white noise, and cannot be inverted using classical stochastic integrals. The inversion involving the extended integrals appears at the end of the report. (Author)