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Liftings for abstract valued functions and separable stochastic processes

  • A. Ionescu Tulcea
  • C. Ionescu Tulcea
Article

Summary

In this paper we extend the notion of lifting from real-valued functions to abstract-valued functions (functions with values in a completely regular space). We prove the existence and uniqueness of the “abstract lifting” associated with a given “real lifting”. As an application we show that given a stochastic process with values in a completely regular space, the modification of this process obtained by applying a lifting is always separable.

Keywords

Stochastic Process Probability Theory Mathematical Biology Regular Space Abstract Lift 
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Bibliography

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    Doob, J. L.: Stochastic processes. New York: John Wiley 1953.Google Scholar
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    Ionescu Tulcea, A., and C. Ionescu Tulcea: On the lifting property (II). Representation of linear operators on spaces L r E, 1≦r<∞. J. Math. Mech. 11, 773–796 (1962).Google Scholar
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    — —: Topics in the theory of liftings. Berlin-Heidelberg-New York: Springer 1969.Google Scholar
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    Meyer, P. A.: Probability and potentials. New York: Blaisdell 1966.Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • A. Ionescu Tulcea
    • 1
  • C. Ionescu Tulcea
    • 1
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA

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