Bismut's Way of the Malliavin Calculus for Non-Markovian Semi-groups: An introduction

TL;DR

This paper reviews recent developments in Bismut's Malliavin Calculus for non-Markovian semigroups, connecting it with elliptic pseudo-differential operators, and introduces new insights in Part IV.

Contribution

It provides a comprehensive review of Bismut's Malliavin Calculus for non-Markovian generators and introduces new connections with elliptic pseudo-differential operators.

Findings

Establishes links between Malliavin Calculus and elliptic pseudo-differential operators.

Reviews recent advances in non-Markovian semigroup analysis.

Introduces new theoretical insights in Part IV.

Abstract

We give a review of our recent works related to the Malliavin Calculus of Bismut type for non-Markovian generators. Part IV is new and relates the Malliavin Calculus and the general theory of elliptic pseudo-differential operators.