Constructive martingale representation in functional It\^o calculus: a local martingale extension

TL;DR

This paper extends the constructive martingale representation theorem within functional Itô calculus from square integrable martingales to local martingales, broadening its applicability in stochastic analysis.

Contribution

It introduces a local martingale extension of the constructive martingale representation theorem in functional Itô calculus, expanding the theoretical framework.

Findings

Extended the theorem to local martingales

Maintained the framework within augmented Wiener filtrations

Broadened the scope of functional Itô calculus

Abstract

The constructive martingale representation theorem of functional It\^o calculus is extended, from the space of square integrable martingales, to the space of local martingales. The setting is that of an augmented filtration generated by a Wiener process.