A brief background on Malliavin calculus and white noise analysis

Abstract

Functional analysis provides us with a rich repertoire of algebraic structures as we see later, which could be used to develop models of complex systems having inherent probabilistic aspects to them. As often happens in physical sciences, the development of concepts related to the systems at hand are crucial to understanding the behaviors of systems. Mathematical structures that are employed in the concepts are as important as the concepts themselves, and in many cases, mathematics inspires conceptual developments. (Refer Kulasiri and Kosarwal (2021), Holden et al. (1996), Øksendal (1998), Di Nunno et al. (2019), Holden and Øksendal (2022), in the references.)