On the Existence and Path Properties of Stochastic Integrals.
Abstract
The author studies integrals of the form Y(t) = the integral from 0 to t of VdX, t > or = 0, where X is a process with stationary independent increments while V is an adapted previsible process, thus continuing the work of Ito and Millar. In the case of vanishing Brownian component, the author obtains conditions for existence which are considerably weaker than the classical requirement that (V squared) be a.s. integrable. The author also examines the asymptotic behavior of Y(t) for large and small t, and considers the variation with respect to suitable functions f. The latter leads to investigate nonlinear integrals of the form f(VdX). The whole work is based on extensions of two general martingale-type equalities, due to Esseen and von Bahr and to Dubins and Savage respectively, and on a super-martingale which was discovered and explored in a special case by Dubins and Freedman. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1974
- Accession Number
- AD0779131
Entities
People
- Olav Kallenberg
Organizations
- University of North Carolina at Chapel Hill