The moments of first entrance time distributions

  • Kai Lai Chung
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (volume 104)


If f ij * =1, then the sequence {f ij (n) , n≧1} determines a discrete probability distribution called the first entrance time distribution from i to j. (For i = j this has also already been called the recurrence time distribution of i in §6.) Thus for each p, \(\sum\limits_{N=1}^{\infty }{{{n}^{p}}f\frac{n}{ij}}\) is the moment of order p of this distribution; for p=1 this is the m ij defined in § 9. More generally, let H be the taboo set; we write
$${{H}^{m\begin{matrix}(p)\\ij\\\end{matrix}}}=\sum\limits_{n=1}^{\infty }{{{n}^{p}}}Hf\begin{matrix}(n)\\ij\\\end{matrix}$$


Random Walk Recurrence Time Discrete Parameter Positive Class Tauberian Theorem 
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Copyright information

© Springer-Verlag OHG. Berlin · Göttingen · Heidelberg 1960

Authors and Affiliations

  • Kai Lai Chung
    • 1
  1. 1.Syracuse UniversityUSA

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