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...

وصف كامل

محفوظ في:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: Leduc, Guillaume (author)
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