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Abstract
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 volurne nullification property of a ddimensional 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 flow. We recover the main stability results in [1], [2], and [3] as special cases
1 Research partially supported by grant no. D4276 DAG94/95.SC27.
2 Research partially supported by the Office of Naval Research under the grant N0001496- 1-0263.
1 Research partially supported by grant no. D4276 DAG94/95.SC27.
2 Research partially supported by the Office of Naval Research under the grant N0001496- 1-0263.
Notes
1 Research partially supported by grant no. D4276 DAG94/95.SC27.
2 Research partially supported by the Office of Naval Research under the grant N0001496- 1-0263.