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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Vector-valued stochastic processes. V. Optional and predictable variation of stochastic measures and stochastic processes
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by Nicolae Dinculeanu PDF
Proc. Amer. Math. Soc. 104 (1988), 625-631 Request permission


Let $\mu$ be a stochastic measure, with values in a Banach space $E$, with finite variation $|\mu |$. If $\mu$ is optional (resp. predictable), then $|\mu |$ is also optional (resp. predictable) provided $E$ is separable, or the dual of a separable space, or has the Radon-Nikodym property. Let $A$ be a right continuous stochastic process with values in $E$, with finite variation $|A|$. If $A$ is measurable (resp. optional, predictable), then $|A|$, the continuous part $|A{|^c}$ and the discrete part $|A{|^d}$ have the same property.
    C. Dellacherie and P. Meyer, Probabilities and potentials, Vols. I, II, North-Holland, 1978, 1980.
  • N. Dinculeanu, Vector measures, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189
  • Nicolae Dinculeanu, Vector-valued stochastic processes. I. Vector measures and vector-valued stochastic processes with finite variation, J. Theoret. Probab. 1 (1988), no. 2, 149–169. MR 938256, DOI 10.1007/BF01046932
  • Nicolae Dinculeanu, Vector valued stochastic processes. III. Projections and dual projections, Seminar on Stochastic Processes, 1987 (Princeton, NJ, 1987) Progr. Probab. Statist., vol. 15, Birkhäuser Boston, Boston, MA, 1988, pp. 93–122. MR 1046412, DOI 10.1007/978-1-4684-0550-7_{4}
  • A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 48, Springer-Verlag New York, Inc., New York, 1969. MR 0276438
  • Michel Métivier, Semimartingales, de Gruyter Studies in Mathematics, vol. 2, Walter de Gruyter & Co., Berlin-New York, 1982. A course on stochastic processes. MR 688144
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 104 (1988), 625-631
  • MSC: Primary 60G07; Secondary 60G57
  • DOI:
  • MathSciNet review: 962839