Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Vector-valued stochastic processes. V. Optional and predictable variation of stochastic measures and stochastic processes

Author: Nicolae Dinculeanu
Journal: Proc. Amer. Math. Soc. 104 (1988), 625-631
MSC: Primary 60G07; Secondary 60G57
MathSciNet review: 962839
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mu $ be a stochastic measure, with values in a Banach space $ E$, with finite variation $ \vert\mu \vert$. If $ \mu $ is optional (resp. predictable), then $ \vert\mu \vert$ 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 $ \vert A\vert$. If $ A$ is measurable (resp. optional, predictable), then $ \vert A\vert$, the continuous part $ \vert A{\vert^c}$ and the discrete part $ \vert A{\vert^d}$ have the same property.

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

  • [1] C. Dellacherie and P. Meyer, Probabilities and potentials, Vols. I, II, North-Holland, 1978, 1980.
  • [2] N. Dinculeanu, Vector measures, International Series of Monographs in Pure and Applied Mathematics, Vol. 95, Pergamon Press, Oxford-New York-Toronto, Ont.; VEB Deutscher Verlag der Wissenschaften, Berlin, 1967. MR 0206190
  • [3] 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,
  • [4] 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,
  • [5] 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
  • [6] 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60G07, 60G57

Retrieve articles in all journals with MSC: 60G07, 60G57

Additional Information

Keywords: Stochastic processes, stochastic measures, finite variation, measurable, optional, predictable, Banach space
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society