On non-continuous Dirichlet processes
type: Item
instance of: scholarly article
title: On non-continuous Dirichlet processes
zbMATH Open document ID: 1026.60072
DOI: 10.1023/A:1022238723289
author: François Coquet
author: Jean Mémin
author: Leszek Slominski
published in: Journal of Theoretical Probability
publication date: 2003-04-27T00:00:00Z
review text: A Dirichlet process is an adapted càdlàg process that can be represented as the sum of a semimartingale and an adapted continuous process with zero quadratic variation. For continuous Dirichlet processes, a pathwise Itô calculus was introduced by \textit{H. Föllmer} [in: Séminaire de probabilités XV. Lect. Notes Math. 850, 143-150 (1981; Zbl 0461.60074) and in: Stochastic integrals. Lect. Notes Math. 851, 476-478 (1981; Zbl 0462.60046)]. In the paper under review, such results are obtained for non-continuous Dirichlet processes. In particular, it is shown that the class of Dirichlet processes is stable under \(C^1\) transforms.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 1901507
zbMATH Keywords: Dirichlet process
zbMATH Keywords: pathwise Itô calculus
zbMATH Keywords: jump process
reviewed by: Alexander Schied
MaRDI profile type: Publication
Wikidata QID: Q131317071
description: scientific article; zbMATH DE number 1901507