On the Existence and Path Properties of Stochastic Integrals.
NORTH CAROLINA UNIV CHAPEL HILL DEPT OF STATISTICS
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The author studies integrals of the form Yt 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 Yt 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 fVdX. 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
- Statistics and Probability