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Absolute Continuity of Diffusion Bridges

Paul McGill ()
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Paul McGill: Université Claude Bernard Lyon 1

Sankhya B: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 2, 240-246

Abstract: Abstract Given a Brownian motion (bt) and ϕ : ℝ → ℝ $\phi : {\mathbb {R}} \to {\mathbb {R}}$ of finite variation on compacts, the SDE z ′ = b ′ − ϕ ( z ) $ z^{\prime } = b^{\prime } - \phi (z) $ determines a unique regular diffusion. We establish equivalence of their bridge laws on ℂ ( [ 0 , 1 ] ) ${\mathbb {C}}([0,1])$ 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; Primary 60J65; Secondary 60H10; 28C20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13571-018-0184-z

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Handle: RePEc:spr:sankhb:v:82:y:2020:i:2:d:10.1007_s13571-018-0184-z