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Contents of PMS, Vol. 5, Fasc. 2,
pages 197 - 209
 

JUMPS OF STOCHASTIC PROCESSES WITH VALUES IN A TOPOLOGICAL GROUP

Eberhard Siebert

Abstract: We consider a stochastic process X taking its values in a Polish group G and having independent increments. First we investigate the jump measures v t on G associated with the process X . Then we identify the measures v t with the Lévy measures of certain convolution semigroups on G closely connected with X. Finally we show that for a submultiplicative function f on G the integrability with respect to the process X is essentially equivalent with the integrability of f with respect to the jump measures v t of X.

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

Key words and phrases: -

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