# A Note on Absolutely Continuous Processes

## TL;DR

This paper discusses the properties of adapted absolutely continuous processes, showing they have predictable densities and can be represented as integrals of locally integrable processes, clarifying their structure in stochastic analysis.

## Contribution

It establishes the equivalence between adapted absolutely continuous processes and integrals of predictable locally integrable processes, providing a clearer understanding of their structure.

## Key findings

- Every adapted absolutely continuous process has a predictable density.
- Such processes are equivalent to time integrals of predictable locally integrable processes.
- The set of these processes can be characterized precisely.

## Abstract

Every adapted absolutely continuous process has a predictable density. The set of adapted absolutely continuous processes equals the set of time integrals of progressive or predictable pathwise locally integrable processes.