Cox, A. M. G., Hobson, David (David G.) and Obłój, Jan (2011) Time-homogeneous diffusions with a given marginal at a random time. ESAIM: Probability and Statistics, Vol.15 . S11-S24. doi:10.1051/ps/2010021 ISSN 1292-8100.

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Abstract

We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) is specified via its speed measure m. We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, Ann. Probab. 20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give a proof exploiting applications of Krein's spectral theory of strings to the study of linear diffusions. Finally, we present a novel direct probabilistic proof based on a coupling argument.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH):	Diffusion processes, Probability measures
Journal or Publication Title:	ESAIM: Probability and Statistics
Publisher:	Cambridge University Press
ISSN:	1292-8100
Official Date:	2011
Dates:	Date Event 2011 Published
Volume:	Vol.15
Page Range:	S11-S24
DOI:	10.1051/ps/2010021
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	20 December 2015
Date of first compliant Open Access:	20 December 2015
Funder:	Sixth Framework Programme (European Commission) (FP6), Oxford-Man Institute of Quantitative Finance

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