Lévy measure of superprocesses; absorption processes

E. B. Dynkin
Additional contact information
E. B. Dynkin: Cornell University, Department of Mathematics

A chapter in Itô’s Stochastic Calculus and Probability Theory, 1996, pp 1-14 from Springer

Abstract: Summary We prove that the (modified) Lévy measure of a superprocess X is the lifting of its discontinuous branching characteristic. We also investigate, for a wide class of functions f, the continuous martingale part of process . (For time-homogeneous processes with local branching, similar results have been obtained earlier by El Karoui and Roelly.) We use the expression for the Lévy measure to establish the predictability of absorption processes. For a particle system, an absorption process can be obtained by freezing every particle at the first exit from a subset Q in the product of time interval and state space. The mass distribution X t ’ of particles frozen during time interval [0, t] is a measure on the complement of Q. The monotone increasing measure-valued process Xt is called an absorption process. A process of this kind can be constructed for every superprocess X in E and every finely open Borel subset Q of ℝ+ × E. In a recent paper by Dynkin and Kuznetsov, absorption processes have been used to describe linear additive functionals of superprocesses.

Keywords: Markov Process; Absorption Process; Random Measure; Borel Function; Additive Functional (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-4-431-68532-6_1

Ordering information: This item can be ordered from
http://www.springer.com/9784431685326

DOI: 10.1007/978-4-431-68532-6_1

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().