Asymptotic behaviour of certain martingales with values in a Riemannian manifold
type: Item
instance of: scholarly article
title: Asymptotic behaviour of certain martingales with values in a Riemannian manifold
zbMATH Open document ID: 0920.58063
DOI: 10.1016/S0007-4497(98)80172-3
author: Jean-Louis Ducourtioux
published in: Bulletin des Sciences Mathématiques
publication date: 1999-09-10T00:00:00Z
review text: The author studies the asymptotic behaviour [see also \textit{J.-J. Prat}, C. R. Acad. Sci., Paris, Sér. A 280, 1539-1542 (1975; Zbl 0309.60052)] of the bounded dilation martingales [see also \textit{W. S. Kendall}, Lect. Notes Math. 851, 479-491 (1981; Zbl 0467.60072)], or of the quasi-conformal martingales [see also \textit{S. I. Goldberg} and \textit{C. Mueller}, Bull. Am. Math. Soc., New Ser. 7, 259-263 (1982; Zbl 0501.58016)] with values in a Riemannian manifold. The main idea is that after translation and conditioning with a stopping time the upper processes are also martingales with the same features. The author also uses a comparison method [see also \textit{P. Malliavin}, Proc. Natl. Acad. Sci. USA 71, 381-383 (1974; Zbl 0449.60040)]. Theorems of almost sure convergence of martingales with values in a Riemannian manifold and a generalization of Picard's little theorem on stochastically complete Riemannian manifolds are given.
reviewed by: Mihai Gradinaru
Mathematics Subject Classification ID: 58J65
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 32H25
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 60J45
zbMATH DE Number: 1202433
zbMATH Keywords: bounded dilation martingales
zbMATH Keywords: quasi-conformal martingales
zbMATH Keywords: stochastically complete Riemannian manifold
zbMATH Keywords: Picard's little theorem
MaRDI profile type: Publication
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full work available at URL: s0007-4497(98)80172-3
OpenAlex ID: W1999068604
description: scientific article; zbMATH DE number 1202433