Girsanov identities for Poisson measures under quasi-nilpotent transformations
We prove a Girsanov identity on the Poisson space for anticipating transformations that satisfy a strong quasi-nilpotence condition. Applications are given to the Girsanov theorem and to the invariance of Poisson measures under random transformations. The proofs use combinatorial identities for the...
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| Format: | Article |
| Language: | English |
| Published: |
2013
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| Online Access: | https://hdl.handle.net/10356/80116 http://hdl.handle.net/10220/10219 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | We prove a Girsanov identity on the Poisson space for anticipating transformations that satisfy a strong quasi-nilpotence condition. Applications are given to the Girsanov theorem and to the invariance of Poisson measures under random transformations. The proofs use combinatorial identities for the central moments of Poisson stochastic integrals. |
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