Additive Processes on Local Fields

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 3, Page 629--654.

Yasuda, Kumi
Additive Processes on Local Fields
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The present paper aims at investigating some basic properties of additive processes on local fields which are rotation- invariant, i.e., invariant under multiplications by any elements of norm 1. We will give the transition probabilities of such processes explicitly, and prove that each process is a limit of processes expressed as integrals. The Lévy measures of their transition probabilities will be used to tell whether they are recurrent, and whether they are stable. For stable processes, we will give some detailed observations.

Mathematics Subject Classification (1991): Primary 60G07; Secondary 11S15
Mathematical Reviews Number: MR1432111

Received: 1995-03-31