Time-Homogeneous Diffusions with a Given Marginal at a Random Time
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 sh...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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2009
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| _version_ | 1797105407571787776 |
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| author | Cox, A Hobson, D Obloj, J |
| author_facet | Cox, A Hobson, D Obloj, J |
| author_sort | Cox, A |
| collection | OXFORD |
| description | 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 strings to the study of linear diffusions. Finally, we present a novel direct probabilistic proof based on a coupling argument. |
| first_indexed | 2024-03-07T06:47:06Z |
| format | Journal article |
| id | oxford-uuid:fb3ca2e9-573a-41e5-8cb0-dbae3cd1925d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:47:06Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:fb3ca2e9-573a-41e5-8cb0-dbae3cd1925d2022-03-27T13:12:14ZTime-Homogeneous Diffusions with a Given Marginal at a Random TimeJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fb3ca2e9-573a-41e5-8cb0-dbae3cd1925dEnglishSymplectic Elements at Oxford2009Cox, AHobson, DObloj, JWe 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 strings to the study of linear diffusions. Finally, we present a novel direct probabilistic proof based on a coupling argument. |
| spellingShingle | Cox, A Hobson, D Obloj, J Time-Homogeneous Diffusions with a Given Marginal at a Random Time |
| title | Time-Homogeneous Diffusions with a Given Marginal at a Random Time |
| title_full | Time-Homogeneous Diffusions with a Given Marginal at a Random Time |
| title_fullStr | Time-Homogeneous Diffusions with a Given Marginal at a Random Time |
| title_full_unstemmed | Time-Homogeneous Diffusions with a Given Marginal at a Random Time |
| title_short | Time-Homogeneous Diffusions with a Given Marginal at a Random Time |
| title_sort | time homogeneous diffusions with a given marginal at a random time |
| work_keys_str_mv | AT coxa timehomogeneousdiffusionswithagivenmarginalatarandomtime AT hobsond timehomogeneousdiffusionswithagivenmarginalatarandomtime AT oblojj timehomogeneousdiffusionswithagivenmarginalatarandomtime |