Martingale problem for superprocesses with non-classical branching functional
The martingale problem for superprocesses with parameters (, Ф, ) is studied where () may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of martingale problem: we show that for any process X which partially solves the martingale probl...
محفوظ في:
| المؤلف الرئيسي: | |
|---|---|
| التنسيق: | article |
| منشور في: |
2006
|
| الموضوعات: | |
| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/16671 |
| الوسوم: |
إضافة وسم
لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!
|
| _version_ | 1864513437563879424 |
|---|---|
| author | Leduc, Guillaume |
| author_facet | Leduc, Guillaume |
| author_role | author |
| dc.creator.none.fl_str_mv | Leduc, Guillaume |
| dc.date.none.fl_str_mv | 2006 2020-06-03T07:48:56Z 2020-06-03T07:48:56Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Leduc Guillaume, "Martingale problem for superprocesses with non-classical branching functional", Stochastic Processes and their Applications 116 (2006), no. 10, 1468-1495. 0304-4149 http://hdl.handle.net/11073/16671 doi.org/10.1016/j.spa.2006.03.005 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.relation.none.fl_str_mv | https://doi.org/10.1016/j.spa.2006.03.005 |
| dc.subject.none.fl_str_mv | Superprocesses Martingale problem Branching functional Dawson–Girsanov transformation Superprocess with interactions |
| dc.title.none.fl_str_mv | Martingale problem for superprocesses with non-classical branching functional |
| dc.type.none.fl_str_mv | Peer-Reviewed Published version info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | The martingale problem for superprocesses with parameters (, Ф, ) is studied where () may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of martingale problem: we show that for any process X which partially solves the martingale problem, an extended form of the liftings defined in [8] exists; these liftings are part of the statement of the full martingale problem, which is hence not defined for processes X who fail to solve the partial martingale problem. The existence of a solution to the martingale problem follows essentially from Itô’s formula. The proof of uniqueness requires that we find a sequence of (, Ф, ) -superprocesses “approximating” the (, Ф, )-superprocess, where () has the form λ (,). Using an argument in [9], applied to the (, Ф, )-superprocesses, we prove, passing to the limit, that the full martingale problem has a unique solution. This result is applied to construct superprocesses with interactions via a Dawson–Girsanov transformation. |
| format | article |
| id | aus_021795b339507fdbe045f2a02e03bce8 |
| identifier_str_mv | Leduc Guillaume, "Martingale problem for superprocesses with non-classical branching functional", Stochastic Processes and their Applications 116 (2006), no. 10, 1468-1495. 0304-4149 doi.org/10.1016/j.spa.2006.03.005 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/16671 |
| publishDate | 2006 |
| publisher.none.fl_str_mv | Elsevier |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Martingale problem for superprocesses with non-classical branching functionalLeduc, GuillaumeSuperprocessesMartingale problemBranching functionalDawson–Girsanov transformationSuperprocess with interactionsThe martingale problem for superprocesses with parameters (, Ф, ) is studied where () may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of martingale problem: we show that for any process X which partially solves the martingale problem, an extended form of the liftings defined in [8] exists; these liftings are part of the statement of the full martingale problem, which is hence not defined for processes X who fail to solve the partial martingale problem. The existence of a solution to the martingale problem follows essentially from Itô’s formula. The proof of uniqueness requires that we find a sequence of (, Ф, ) -superprocesses “approximating” the (, Ф, )-superprocess, where () has the form λ (,). Using an argument in [9], applied to the (, Ф, )-superprocesses, we prove, passing to the limit, that the full martingale problem has a unique solution. This result is applied to construct superprocesses with interactions via a Dawson–Girsanov transformation.Elsevier2020-06-03T07:48:56Z2020-06-03T07:48:56Z2006Peer-ReviewedPublished versioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfLeduc Guillaume, "Martingale problem for superprocesses with non-classical branching functional", Stochastic Processes and their Applications 116 (2006), no. 10, 1468-1495.0304-4149http://hdl.handle.net/11073/16671doi.org/10.1016/j.spa.2006.03.005en_UShttps://doi.org/10.1016/j.spa.2006.03.005oai:repository.aus.edu:11073/166712024-08-22T12:02:04Z |
| spellingShingle | Martingale problem for superprocesses with non-classical branching functional Leduc, Guillaume Superprocesses Martingale problem Branching functional Dawson–Girsanov transformation Superprocess with interactions |
| status_str | publishedVersion |
| title | Martingale problem for superprocesses with non-classical branching functional |
| title_full | Martingale problem for superprocesses with non-classical branching functional |
| title_fullStr | Martingale problem for superprocesses with non-classical branching functional |
| title_full_unstemmed | Martingale problem for superprocesses with non-classical branching functional |
| title_short | Martingale problem for superprocesses with non-classical branching functional |
| title_sort | Martingale problem for superprocesses with non-classical branching functional |
| topic | Superprocesses Martingale problem Branching functional Dawson–Girsanov transformation Superprocess with interactions |
| url | http://hdl.handle.net/11073/16671 |