# The moments of first entrance time distributions

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

## Abstract

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
$${{H}^{m\begin{matrix}(p)\\ij\\\end{matrix}}}=\sum\limits_{n=1}^{\infty }{{{n}^{p}}}Hf\begin{matrix}(n)\\ij\\\end{matrix}$$

## Keywords

Random Walk Recurrence Time Discrete Parameter Positive Class Tauberian Theorem
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.