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Proceedings of the American Mathematical Society

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Functions of Brownian motion


Author: John B. Walsh
Journal: Proc. Amer. Math. Soc. 49 (1975), 227-231
MSC: Primary 60J65
DOI: https://doi.org/10.1090/S0002-9939-1975-0362520-3
MathSciNet review: 0362520
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Abstract: The class of continuous functions $ h$ for which $ h$ (Brownian motion) is a Markov process is determined.


References [Enhancements On Off] (What's this?)

  • [1] R. M. Dudley, Non-linear equivalence transformations of Brownian motion, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 20 (1971), 249-258. MR 46 # 6485. MR 0307365 (46:6485)
  • [2] E. B. Dynkin, Markov processes, Fizmatgiz, Moscow, 1963; English transl., Vols. I, II, Die Grundlehren der math. Wissenschaften, Bände 121, 122, Academic Press, New York; Springer-Verlag, Berlin, 1965. MR 33 # 1886; # 1887. MR 0193670 (33:1886)
  • [3] K. Itô and H. P. McKean, Diffusion processes and their sample paths, Die Grundlehren der math. Wissenschaften, Band 125, Academic Press, New York; Springer-Verlag, Berlin, 1965. MR 33 # 8031. MR 0199891 (33:8031)
  • [4] M. Rosenblatt, Functions of a Markov process that are Markovian, J. Math. Mech. 8 (1959), 665-681. MR 0103539 (21:2307)

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DOI: https://doi.org/10.1090/S0002-9939-1975-0362520-3
Article copyright: © Copyright 1975 American Mathematical Society

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