The problem of the uniqueness of a martingale
type: Item
instance of: scholarly article
title: The problem of the uniqueness of a martingale
zbMATH Open document ID: 0974.60060
published in: Doklady Mathematics
publication date: 2001-02-13T00:00:00Z
review text: The author considers a martingale problem for uniformly elliptic operator \(L\) with measurable (not necessarily continuous) coefficients. The purpose of the paper is to demonstrate that in the general case, the solution of the martingale problem is not unique. In this connection, he considers the Dirichlet problem for the operator \(L\). According to Stroock and Varadhan, if the solution to the Dirichlet problem is not unique, then the solution of the corresponding martingale problem is not unique also. The main result is that in the unit ball \(B_1\subset\mathcal{R}^3\) there exist such operator \(L\) and such boundary condition that the solution of the corresponding Dirichlet problem is not unique.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60G44
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1564538
zbMATH Keywords: martingale problem
zbMATH Keywords: elliptic operator
zbMATH Keywords: measurable coefficients
zbMATH Keywords: Dirichlet problem
author: Nikolai Nadirashvili
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1564538