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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  
Dates: 


Volume:  Vol.15  
Page Range:  S11S24  
Identifier:  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) 
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