Advertisement

Annali di Matematica Pura ed Applicata

, Volume 71, Issue 1, pp 85–92 | Cite as

On stochastic processes whose trajectories have no discontinuities of the second kind

  • Harald Carmér
Article

Summary

It is shown that, under the condition(1) below, the trajectories of the stochastic process ζ(t) can, after replacing the ζ(t) process by an equivalent version η(t), at most have discontinuities of the first kind, i.e. simple jumps.

Keywords

Stochastic Process Equivalent Version Simple Jump 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. [1]
    Yu. K. Belajev,Continuity and Hölder's conditions for sample functions of stationary Gaussian processes, Proc. Fourth Berkeley Symp, 2 (1961), 23–33.Google Scholar
  2. [2]
    N. N. Chentsov,Weak convergence of stochastic processes whose trajectories have no discontinuities of the second kind and the heuristic approach to the Kolmogorov-Smirnoff tests, Teor. Verojatnost. i Primenen., 1 (1956), 140–144.Google Scholar
  3. [3]
    H. Cramér,Mathematical Methods of Statistics, Princeton Univ. Press., 1946.Google Scholar
  4. [4]
    R. L. Dobruschin,The continuity condition for sample functions of a martingale, Teor. Verojatnost. i Primenen, 3 (1958), 92–93.Google Scholar
  5. [5]
    E. B. Dynkin,Criteria of continuity and of absence of discontinuities of the second kind for trajectories of a Markov random process, Izv. A kad. Nauk SSSR, 16 (1952), 563–572.zbMATHMathSciNetGoogle Scholar
  6. [6]
    G. A. Hunt,Random Fourier Transforms, Trans. Amer. Math. Soc., 71 (1951), 38–69.CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    M. Loève,Probability Theory, 2nd Ed., Van Nostrand, Princeton, 1960.Google Scholar
  8. [8]
    E. Slutsky,Qualche proposizione relativa alla teoria delle funzioni aleatorie, Giornale dell'Ist. Italiano degli Attuari, 8 (1937), 193–199.Google Scholar

Copyright information

© Nicola Zanichelli Editore 1966

Authors and Affiliations

  • Harald Carmér
    • 1
  1. 1.Stockholm

Personalised recommendations