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Stochastic multiplicative measures, generalized Markov semigroups, and group-valued stochastic processes and fields. (English) Zbl 0639.60010

Authors’ summary: We extend the well-known relation between Markov semigroups and processes with independent increments to the case of generalized group-valued semigroups indexed by some measurable space and stochastic multiplicative measures. We give a Kolmogorov-type theorem and a classification theorem, connecting the stochastic multiplicative measures with vector-valued Lévy-Khinchine fields.
The results have applications to the study of stochastic connections and differential equations for forms on Lie groups.
Reviewer: Sun Shanli

MSC:

60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60J99 Markov processes
60G20 Generalized stochastic processes
60H99 Stochastic analysis
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