Integration Order Replacement Technique for Iterated Ito Stochastic Integrals and Iterated Stochastic Integrals With Respect to Martingales

Abstract

The article is devoted to the integration order replacement technique for iterated Ito stochastic integrals and iterated stochastic integrals with respect to martingales. We consider the class of iterated Ito stochastic integrals, for which with probability 1 the formulas of integration order replacement corresponding to the rules of classical integral calculus are reasonable. The theorems on integration order replacement for the class of iterated Ito stochastic integrals is proven. Many examples of this theorems usage have been considered. These results are generalized for the class of iterated stochastic integrals with respect to martingales.