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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. 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

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:

1292-8100

Official Date:

2011

Dates:

Date	Event
2011	Published

Volume:

Vol.15

Page Range:

S11-S24

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), Oxford-Man Institute of Quantitative Finance

References:

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