dc.contributor.author | Leduc, Guillaume | |
dc.date.accessioned | 2020-06-03T07:48:56Z | |
dc.date.available | 2020-06-03T07:48:56Z | |
dc.date.issued | 2006 | |
dc.identifier.citation | Leduc Guillaume, "Martingale problem for superprocesses with non-classical branching functional", Stochastic Processes and their Applications 116 (2006), no. 10, 1468-1495. | en_US |
dc.identifier.issn | 0304-4149 | |
dc.identifier.uri | http://hdl.handle.net/11073/16671 | |
dc.description.abstract | The martingale problem for superprocesses with parameters (𝛏, Ф, 𝑘) is studied where 𝑘(𝒹𝑠) 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 (𝛏, Ф, 𝑘𝑛) -superprocesses “approximating” the (𝛏, Ф, 𝑘)-superprocess, where 𝑘𝑛(𝒹𝑠) has the form λ𝑛 (𝑠,𝛏𝑠)𝒹𝑠. Using an argument in [9], applied to the (𝛏, Ф, 𝑘𝑛)-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. | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | Elsevier | en_US |
dc.relation.uri | https://doi.org/10.1016/j.spa.2006.03.005 | en_US |
dc.subject | Superprocesses | en_US |
dc.subject | Martingale problem | en_US |
dc.subject | Branching functional | en_US |
dc.subject | Dawson–Girsanov transformation | en_US |
dc.subject | Superprocess with interactions | en_US |
dc.title | Martingale problem for superprocesses with non-classical branching functional | en_US |
dc.type | Peer-Reviewed | en_US |
dc.type | Article | en_US |
dc.type | Published version | en_US |
dc.identifier.doi | doi.org/10.1016/j.spa.2006.03.005 | |