Abstract
We give a general group theoretic scheme for obtaining intertwining relations between Markov semi-groups. This is applied to the Heisenberg group and yields an intertwining relation between the Ornstein-Uhlenbeck and the Yule semi-groups.
Keywords
- Heisenberg Group
- Abelian Subgroup
- Positive Definite Function
- Markov Kernel
- Gelfand Pair
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References
[A-N] K. B. Athreya and P. E. Ney, Branching processes, Springer verlag, Berlin, Heidelberg, New York, 1972.
[B] P. Biane, Quelques propriétés du mouvement brownien non-commutatif, preprint, Laboratoire de Probabilités, Université Paris VI, 1994.
[C-P-Y] P. Carmona, F. Petit, M. Yor, Beta-gamma random variables and intertwining relations between certain Markov processes, preprint, Laboratoire de Probabilités, Université Paris VI, 1994.
[P] K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs in Mathematics, Vol 85, Birkhäuser, Basel, 1992.
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© 1995 Springer-Verlag
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Biane, P. (1995). Intertwining of Markov semi-groups, some examples. In: Azéma, J., Emery, M., Meyer, P.A., Yor, M. (eds) Séminaire de Probabilités XXIX. Lecture Notes in Mathematics, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094197
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DOI: https://doi.org/10.1007/BFb0094197
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