Decomposition of Convolution Semigroups on Groups and the 0-1 Law

• Autorzy: Byczkowska H. , Byczkowski T.
• Języki publikacji: EN

Abstrakty

EN

Let (X(t))_t>0, be a stochastically continuous symmetric Lévy process with values in a complete separable group G. We denote by (μ_t)_t>0 the semigroup of one-dimensional distributions of X(t). Suppose that H is a Borel subgroup of G such that μ_t (H) > 0 for all t > 0. We obtain a decomposition of the generator of the process X ( t ) into a bounded part concentrated on H^c 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 π (X (t)) on the homogeneous space G/H.

Słowa kluczowe

EN

Lévy process; homogeneous space; convolution semigroups

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 1
• Strony: 97--104
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Byczkowska H.

• Institute of Mathematics, Wrocław Technical University, 50-370 Wrocław, Poland

autor

Byczkowski T.

• Institute of Mathematics, Wrocław Technical University, 50-370 Wrocław, Poland

Bibliografia

• [1] H. Byczkowska and T. Byczkowski, Zero-one low for symmetric convolution semigroups of measures on groups, J. Theoret. Probab. 289 (1998), pp. 633-643.
• [2] T. Byczkowski and A. Hulanicki, Gaussian measure of normal subgroups, Ann. Probab. 11 (1983), pp. 685-691.
• [3] M. Loève, Probability Theory, Part II, Springer, New York 1978.
• [4] E. Siebert, Decomposition of convolution semigroups on Polish groups and zero-one law,Hokkaido Math. J. 16 (1987), pp. 235-255.