Polylinear additive functionals of superprocesses
type: Item
instance of: scholarly article
title: Polylinear additive functionals of superprocesses
zbMATH Open document ID: 0883.60071
author: E. B. Dynkin
published in: Journal of Functional Analysis
publication date: 1998-03-16T00:00:00Z
review text: The author has already studied the linear additive functionals of superprocesses in a previous work [Trans. Am. Math. Soc. 314, No. 1, 255-282 (1989; Zbl 0674.60070)]. But the study of self-intersection local times and \(k\)-multiple points of superprocesses raised the question of polylinear additive functionals. If \(X\) is a superdiffusion in a domain \(E\) of \(\mathbb{R}^d\), a polylinear additive functional of \(X\) corresponding to a positive Borel function \(\rho\) on \((\mathbb{R}_+\times E)^k\) is given by integrating \(\rho\) with respect to the kernel \(X_{t_1}(dz_1)\otimes\cdots\otimes X_{t_k}(dz_k)\), and a general polylinear additive functional is obtained by a passage to the limit from functionals of the previous form. The properties of such functionals are investigated, and an application to self-intersection local times of order \(k\) is given.
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 1054131
zbMATH Keywords: superprocess
zbMATH Keywords: self-intersection local time
zbMATH Keywords: polylinear additive functions
reviewed by: Dominique Lépingle
MaRDI profile type: Publication
OpenAlex ID: W1990757365
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DOI: 10.1006/JFAN.1996.3075
description: scientific article; zbMATH DE number 1054131