The problem of the uniqueness of a martingale
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.
scientific article; zbMATH DE number 1564538