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Abstract

Let (p ij ) be a standard transition matrix. The derivatives at zero of the p ij established in the preceding section are of basic importance in the study of the associated Markov chain. The following notation so will be used throughout the rest of this monograph:
$${{q}_{i}}=-p{{\prime }_{ii}}\left( 0 \right),~ {{q}_{ij}}=p{{\prime }_{ij}}\left( 0 \right),~i\ne j$$
(1)
foil Occasionally the notation q ii =−q i will also be used; the matrix will then be called the Q-matrix of the matrix
$$\left( {{q}_{ij}} \right)=\left( p{{\prime }_{ij}}\left( 0 \right) \right)$$
will then be called the Q-matrix of the matrix(p ij ).

Keywords

Transition Matrix Continuous Parameter Continuous Derivative Preceding Proof General State Space 
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.

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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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