Random sampling from a continuous parameter stochastic process

  • Julius R. Blum
  • Russell A. Boyles
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)


Let {X(t),−∞<t<∞} be a continuous parameter, stationary, ergodic process. We consider random sampling times {τn} and show that for certain of these, if we can observe the bivariate process {τn,X(τn)} we are able to estimate consistently all finite-dimensional distributions of the process {X(t)}.


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  1. [1]
    Blum, J.R. and Rosenblatt, Judah, On Random Sampling From A Stochastic Process, Ann. Math. Statist., 35, (1964), 1713–1717.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Doob, J.L., Stochastic Processes Depending On A Continuous Parameter, Trans. Am. Math. Soc., 42 (1937), 107–140.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Doob, J.L., Stochastic Processes, John Wiley, New York, 1953.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Julius R. Blum
    • 1
  • Russell A. Boyles
    • 1
  1. 1.Division of StatisticsUniversity of CaliforniaDavis

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