A functional Itō-formula for Dawson–Watanabe superprocesses

Christian Mandler and Ludger Overbeck

Stochastic Processes and their Applications, 2022, vol. 144, issue C, 202-228

Abstract: We derive an Itō-formula for the Dawson–Watanabe superprocess, a well-known class of measure-valued processes, extending the classical Itō-formula with respect to two aspects. Firstly, we extend the state–space of the underlying process (X(t))t∈[0,T] to an infinite-dimensional one — the space of finite measure. Secondly, we extend the formula to functions F(t,Xt) depending on the entire paths Xt=(X(s∧t))s∈[0,T] up to times t. This later extension is usually called functional Itō-formula. Finally we remark on the application to predictable representation for martingales associated with superprocesses.

Keywords: Functional Itō-Formula; Dawson–Watanabe superprocesses; Measure-valued diffusion; Non-anticipative path differentiation; Dupire formula; Predictable representation (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414921001848
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:144:y:2022:i:c:p:202-228

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2021.11.003

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().