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Contents of PMS, Vol. 19, Fasc. 1,
pages 97 - 104
 

DECOMPOSITION OF CONVOLUTION SEMIGROUPS ON GROUPS AND THE 0-1 LAW

H. Byczkowska
T. Byczkowski

Abstract: Let (X(t)) t>0 be a stochastically continuous symmetric Lévy process with values in a complete separable group G. We denote by (m) tt>0 the semigroup of one-dimensional distributions of X(t). Suppose that H is a Borel subgroup of G such that m (H) > 0 t for all t > 0. We obtain a decomposition of the generator of the process X(t) into a bounded part concentrated on Hc and the generator of a semigroup concentrated on H. This yields the 0- 1 law for such processes. We also examine the differentiation of transition probability of the induced Markov process p(X(t)) on the homogeneous space G/H.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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