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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Functions of Brownian motion


Author: John B. Walsh
Journal: Proc. Amer. Math. Soc. 49 (1975), 227-231
MSC: Primary 60J65
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 0307365
  • [2] E. B. Dynkin, Markovskie protsessy, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1963 (Russian). MR 0193670
  • [3] Kiyoshi Itô and Henry P. McKean Jr., Diffusion processes and their sample paths, Die Grundlehren der Mathematischen Wissenschaften, Band 125, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-New York, 1965. MR 0199891
  • [4] M. Rosenblatt, Functions of a Markov process that are Markovian, J. Math. Mech. 8 (1959), 585–596. MR 0103539

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