Some properties of path measures

TL;DR

This paper explores properties of path measures, focusing on notions arising naturally in the context of the Schrödinger problem, and provides detailed analysis of these concepts.

Contribution

It introduces and elaborates on fundamental properties of path measures relevant to the Schrödinger problem, offering new insights into their structure.

Findings

Clarifies key notions of path measures in Schrödinger problems

Provides detailed mathematical properties of path measures

Lays groundwork for further research in stochastic processes

Abstract

We call any measure on a path space, a path measure. Some notions about path measures which appear naturally when solving the Schr\"odinger problem are presented and worked out in detail.