Title

Uniqueness of the martingale problem for some degenerate elliptic operators

Date of Completion

January 2004

Keywords

Mathematics

Degree

Ph.D.

Abstract

Let αi ∈ (0, 1), i = 1,…,d. We consider the operator L on C2( Rd ) defined by Lfx= i=1

    d
aix xia i62f6x 2ix +i=1
    d
bi x6f6x ix, x∈Rd, where ai,bi : Rd→ R . ^ We prove existence and uniqueness of the solution of the martingale problem for the operator L under suitable conditions on the functions ai, bi. ^