Martingale characterizations of increment processes in a locally compact group

Heyer, Herbert and Pap, Gyula (2003) Martingale characterizations of increment processes in a locally compact group. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 6 (4). pp. 563-595. ISSN 0219-0257

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Abstract

Martingale characterizations and the related martingale problem are studied for processes with independent (not necessarily stationary) increments in an arbitrary locally compact group. In the special case of a compact Lie group, a Levy-type characterization is given in terms of a faithful finite dimensional representation of the group and its tensor square. For the proofs noncommutative Fourier theory is applied for the convolution hemigroups associated with the increment processes.

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