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Two-parameter Lévy processes: ItÔ formula, semigroups, and generators

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Abstract

We consider random Lévy fields, i.e., stationary fields continuous in probability and having independent increments. We prove that the trajectories of such fields have at most one jump on every line parallel to the axes. We derive an expression for the ItÔ change of variables for Lévy fields. We also consider semigroups generated by Lévy fields and their generators.

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Authors and Affiliations

  1. Kiev University, Kiev

    Yu. S. Mishura

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  1. Yu. S. Mishura
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Published in Ukrainskii Matematicheskii Zhurnal, Vol.47, No. 7, pp. 952–961, July, 1995.

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Mishura, Y.S. Two-parameter Lévy processes: ItÔ formula, semigroups, and generators. Ukr Math J 47, 1092–1102 (1995). https://doi.org/10.1007/BF01084905

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  • DOI: https://doi.org/10.1007/BF01084905

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