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Time-Homogeneous Diffusions with a Given Marginal at a Random Time

Abstract:

We solve explicitly the following problem: for a given probability measure mu, we specify a generalised martingale diffusion X which, stopped at an independent exponential time T, is distributed according to mu. The process X is specified via its speed measure m. We present three proofs. First we show how the result can be derived from the solution of Bertoin and Le Jan (1992) to the Skorokhod embedding problem. Secondly, we give a proof exploiting applications of Krein's spectral theory of s...

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Publication status:
Published

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Publisher copy:
10.1051/ps/2010021
Journal:
ESAIM-PROBABILITY AND STATISTICS More from this journal
Volume:
15
Pages:
S11-S24
Publication date:
2009-12-09
DOI:
EISSN:
1262-3318
ISSN:
1292-8100
Language:
English
Keywords:
Pubs id:
pubs:189170
UUID:
uuid:fb3ca2e9-573a-41e5-8cb0-dbae3cd1925d
Local pid:
pubs:189170
Source identifiers:
189170
Deposit date:
2012-12-19

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