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Applications of Symmetry Groups in Markov Processes

In: Probability Measures on Groups X

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  • Joseph Glover

    (University of Florida, Department of Mathematics)

Abstract

Algebraic structures have enjoyed a special role in Markov processes from the very beginning of the subject. Probabilists focussed much of their attention initially on independent increment processes in the group R. Since these processes have convolution semigroups, they are especially amenable to concrete analysis by Fourier techniques. As Markov processes matured, probabilists began to study them in more general settings, and there is often no algebraic structure in evidence on the state space these days. In this article, we will explore methods of introducing algebraic structures on the state space which are naturally associated with the process. In several instances, after an invertible probabilistic transformation, they will become independent increment processes in the new group structure.

Suggested Citation

  • Joseph Glover, 1991. "Applications of Symmetry Groups in Markov Processes," Springer Books, in: Herbert Heyer (ed.), Probability Measures on Groups X, pages 155-168, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4899-2364-6_12
    DOI: 10.1007/978-1-4899-2364-6_12
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