Pinned Diffusions and Markov Bridges

Florian Hildebrandt () and Sylvie Rœlly ()
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Florian Hildebrandt: University of Hamburg
Sylvie Rœlly: Institut für Mathematik der Universität Potsdam

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 906-917

Abstract: Abstract In this article, we consider a family of real-valued diffusion processes on the time interval [0, 1] indexed by their prescribed initial value $$x \in \mathbb {R}$$x∈R and another point in space, $$y \in \mathbb {R}$$y∈R. We first present an easy-to-check condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in y at time $$t=1$$t=1. Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an Itô diffusion? We eventually illustrate our precise answer with several examples.

Keywords: Pinned diffusion; $$\alpha $$ α -Brownian bridge; $$\alpha $$ α -Wiener bridge; Gaussian Markov process; Reciprocal characteristics; 60G15; 60H10; 60J60 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-019-00954-5

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