A generalization of Strassen's functional law of iterated logarithm

  • P. Révész
Article

Summary

Let {aT; T≧0} be a non-decreasing function of T with 0<aTT and let {W(t); t≧0} be a Wiener process. The limit functions of the processes
$$\Gamma _{t,T} (x) = \beta _T (W(t + xa_T ) - W(t)) (0\underline \leqslant x \underline \leqslant 1)$$
where 0≦tT−aT, T>0 and
$$\beta _T = (2a_T (\log Ta_T^{ - 1} + \log \log T))^{ - \tfrac{1}{2}} $$
are characterized. In the case aT=T Strassen's law is obtained as a special case.

Keywords

Stochastic Process Probability Theory Mathematical Biology Limit Function Wiener Process 

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References

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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • P. Révész
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapest VHungary

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