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Timehomogeneous 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) Timehomogeneous diffusions with a given marginal at a random time. ESAIM: Probability and Statistics, Vol.15 . S11S24. ISSN 12928100

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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 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of 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:  12928100 
Official Date:  2011 
Volume:  Vol.15 
Page Range:  S11S24 
Identification Number:  10.1051/ps/2010021 
Status:  Peer Reviewed 
Publication Status:  Published 
Access rights to Published version:  Restricted or Subscription Access 
Funder:  Sixth Framework Programme (European Commission) (FP6), OxfordMan Institute of Quantitative Finance 
References:  [1] J. Bertoin and Y. Le Jan, Representation of measures by balayage from a regular recurrent point. Ann. Probab. 20 (1992) 
URI:  http://wrap.warwick.ac.uk/id/eprint/43695 
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