Support theorem for pinned diffusion processes

TL;DR

This paper establishes a support theorem for pinned diffusion processes using advanced stochastic analysis techniques, extending the theoretical understanding of the behavior of such processes.

Contribution

It introduces a support theorem for pinned diffusions leveraging quasi-sure analysis and positivity results, which are novel applications in this context.

Findings

Proves a support theorem of Stroock-Varadhan type for pinned diffusions

Utilizes quasi-sure analysis for Brownian rough paths

Applies positivity theorem for densities of Wiener functionals

Abstract

In this paper we prove a support theorem of Stroock-Varadhan type for pinned diffusion processes. To this end we use two powerful results from stochastic analysis. One is quasi-sure analysis for Brownian rough path. The other is Aida-Kusuoka-Stroock's positivity theorem for the densities of weighted laws of non-degenerate Wiener functionals.