Alili, Larbi, Graczyk, P. (Piotr) and Żak, Tomasz (2015) On inversions and Doob h-transforms of linear diffusions. In: In memoriam Marc Yor : séminaire de probabilités XLVII. Switzerland: Springer, pp. 107-126. ISBN 9783319185842

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Abstract

Let X be a regular linear diffusion whose state space is an open interval E⊆R. We consider the dual diffusion X ∗ whose probability law is obtained as a Doob h-transform of the law of X, where h is a positive harmonic function for the infinitesimal generator of X on E. We provide a construction of X ∗ as a deterministic inversion I(X) of X, time changed with some random clock. Such inversions generalize the Euclidean inversions that intervene when X is a Brownian motion. The important case where X ∗ is X conditioned to stay above some fixed level is included. The families of deterministic inversions are given explicitly for the Brownian motion with drift, Bessel processes and the three-dimensional hyperbolic Bessel process.

Item Type:	Book Item
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Diffusion processes
Publisher:	Springer
Place of Publication:	Switzerland
ISBN:	9783319185842
ISSN:	0075-8434
Book Title:	In memoriam Marc Yor : séminaire de probabilités XLVII
Official Date:	2015
Dates:	Date Event 2015 Published
Volume:	2137
Page Range:	pp. 107-126
DOI:	10.1007/978-3-319-18585-9_6
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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