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Time-homogeneous diffusions with a given marginal at a random time
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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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Official URL: http://dx.doi.org/10.1051/ps/2010021
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 | ||||
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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: |
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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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