Applications of the Integration by Parts Formula II: An Advance Study

We have formulated our main delay stochastic differential equation in stratonovich form and we have also established some theorems and results which can be regarded as more advanced applications of the integration by parts formula. We have established an integration by parts formula involving Mallivan derivatives of solutions to such type of delay (functional) SDE's. The integration by parts formula which we have established is used here to extend the formulas in [2] and [3] to include delay SDE's as well as ordinary SDE's. in this work we have also established some other useful applications to delay SDE's. Here in this work you will find an extension of the first three chapters of the work of Norris to include delay SDE's as well as ordinary SDE's; see Theorems 2.3, 3.1 and 3.2 in [13].