DECOMPOSITION OF CONVOLUTION SEMIGROUPS ON GROUPS ANDTHE 0-1 LAW

H. Byczkowska T. Byczkowski

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