Quasi-martingales with a linearly ordered index set

TL;DR

This paper extends the Rao decomposition to quasi-martingales indexed by a linearly ordered set, providing a new theoretical framework for analyzing such stochastic processes.

Contribution

It introduces a Rao decomposition for quasi-martingales with a linearly ordered index set, advancing the theoretical understanding of these processes.

Findings

Established Rao decomposition for linearly indexed quasi-martingales

Extended classical martingale theory to more general index sets

Provided foundational results for future research in stochastic processes

Abstract

We prove a version of Rao decomposition for quasi-martingales indexed by a linearly ordered set.