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Sankhya B

pp 1–7 | Cite as

Absolute Continuity of Diffusion Bridges

  • Paul McGillEmail author
Article

Abstract

Given a Brownian motion (bt) and \(\phi : {\mathbb {R}} \to {\mathbb {R}}\) of finite variation on compacts, the SDE \( z^{\prime } = b^{\prime } - \phi (z) \) determines a unique regular diffusion. We establish equivalence of their bridge laws on \({\mathbb {C}}([0,1])\) via absolute continuity for an approximate version – endpoint in a bounded interval. The periodic case facilitates manipulations with circular diffusion measures.

Keywords

Approximate bridge Girsanov formula Circular measure 

AMS (2000) subject classification

Primary 60J65 Secondary 60H10, 28C20 

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Copyright information

© Indian Statistical Institute 2019

Authors and Affiliations

  1. 1.Département de MathématiquesUniversité Claude Bernard Lyon 1VilleurbanneFrance

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