We have developed certain theorems and conclusions that may be regarded as more complex uses of the integration by parts method in addition to formulating our primary delay stochastic differential equation in stratonovich form. We have developed a method for integration by parts that uses Mallivan derivatives as solutions to these kinds of delay (functional) SDEs. The extension of the formulae in [2] and [3] to include delay SDEs in addition to regular SDEs is done here using the integration by parts formula that we have developed. In this study, we have also developed a few other helpful apps to postpone SDEs. The first three chapters of Norris' work are extended in this work to cover delay SDEs as well as regular SDEs; for further information, see Theorems 2.3, 3.1, and 3.2 in [13].
Tagelsir A. Ahmed,
Department of Pure Mathematics, Faculty of Mathematical Science, University, of Khartoum, Khartoum, Sudan.
A. Jan Van Casteren,
Department of Mathematics and Computer Science, University, of Antwerp (UA), Middelheimlaan 1, Antwerp, Belgium.
Please see the link here: https://stm.bookpi.org/NRAMCS-V5/article/view/7491
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