INTEGRATION BY PARTS FORMULA INVOLVING MALLIAVIN DERIVATIVES AND SOLUTIONS TO DELAY SDE’S

In the present work we have established an integration by parts formula of higher order Malliavin derivatives of solutions to delay stochastic differential equations. In a squeal work we will use this integration by parts formula in some applications concerning densities of distributions of solutions of delay (as well as ordinary) stochastic differential equations with possibly discontinuous initial data. Also, this integration by parts formula can be used to extended the formulas in the work by Bally and Talay to include delay as well as ordinary SDE’s.