TANGENTIAL EXISTENCE AND COMPARISON, WITH APPLICATIONS
TO SINGLE AND MULTIPLE INTEGRATION
Abstract: Two semi-martingales with respect to a common filtration are said to be tangential if
they have the same local characteristics. When the latter are non-random, the underlying
semi-martingale is known to have independent increments. We show that every
semi-martingale has a tangential process with conditionally independent increments. We also
extend the Zinn–Hitchenko and related tangential comparison theorems to continuous time.
Combining those results, we obtain some surprisingly general existence, convergence,
and tightness criteria for broad classes of single and multiple stochastic integrals.
2010 AMS Mathematics Subject Classification: Primary: 60G44, 60G57; Secondary:
Keywords and phrases: Tangential processes, local characteristics, conditional
symmetry, marked point processes, compensators, stochastic integration, multiple stochastic