Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 1,pp. 1--11

STABLE PROBABILITY MEASURES ON p-ADIC LIE GROUPS

By

C.R.E. RAJA Tata Institute of Fundamental Research, Mumbai

SUMMARY. In this paper we prove that various concepts of stable measures are equivalent for probability measures on finite-dimensional p-adic vector spaces. We also study Baldi stable measures on p-adic Lie groups and in particular obtain a complete description of them in case of linear groups. A similar characterization is obtained for normal Baldi stable measures on p-adic Lie groups.

AMS (1991) subject classification.Primary 60B15, 60E07; secondary 22E35.

Key words and phrases. Stable measures; continuous convolution semigroups; p-adic Lie groups.

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