Tangential existence and comparison, with applications to single and multiple integration

摘要

Two semi-martingales with respect to a common filtrationare said to be tangential if they have the same local characteristics. Whenthe latter are non-random, the underlying semi-martingale is known to haveindependent increments. We show that every semi-martingale has a tangentialprocess with conditionally independent increments. We also extend theZinn–Hitchenko and related tangential comparison theorems to continuoustime. Combining those results, we obtain some surprisingly general existence,convergence, and tightness criteria for broad classes of single andmultiple stochastic integrals.