Probability Seminar Department of Statistics and Department of Mathematics Monday, February 23, 2004 3:30 PM in MATH 215 Professor Krzysztof Bogdan Polish Academy of Science and Wroclaw University of Technology will speak on Harnack Inequality for Harmonic Functions of Jump Processes Abstract We will give a necessary and sufficient condition for Harnack inequality to hold for nonnegative harmonic functions of certain stable anisotropic processes with independent increments. The condition (on the Levy measure of the process i.e. on the integral kernel of the generator of the process) is called the relative Kato condition. Our results depend on estimates of superharmonic functions especially of the Green function. The talk should be accessible to nonprobabilists (analysts).

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