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Abstract

We shall give in this section a complete determination of the limit or limits of p ij (n) as n → ∞, for every i and j. If j is nonrecurrent it follows already from the Corollary to Theorem 5.5 that \( \mathop {\lim }\limits_{n \to \infty } p_{ij}^{\left( n \right)} = 0. \)

Keywords

Random Walk Ergodic Theorem Great Common Divisor Discrete Parameter Stationary Transition Probability 
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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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