Stability in distribution and volume nullification of Levy flow

We continue our study, Basak and Kannan [3], of Hasminskii's almost sure stability in large of one-dimensional nonsingular diffusions; extending it now to the volume nullification property of a d-dimensional Levy flow (singular or nonsingular). The proof in [3] is extended to account for the jump nature of a Levy process. We first show the stability in distribution. Some moment estimates of the Jacobian matrix of the Levy flow are the technical results established next. These are used to prove the volume- and covolume-nullification properties of the Levy how. We recover the main stability results in [1], [2], and [3] as special cases.