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Keywords:

  • Q-matrices;
  • continuous time Markov chains;
  • positive maximum principle;
  • pseudo-differential operators with negative definite symbols on Zn;
  • estimates for transition functions;
  • msc (2010) 47006;
  • 47007;
  • 47G30;
  • 35S05;
  • 60J35

Abstract

Operators induced by Q-matrices on equation image are shown to satisfy the positive maximum principle and to have a representation as a pseudo-differential operator with symbol equation image which is with respect to the co-variable negative definite (in the sense of Schoenberg). This observation leads already towards a more geometric interpretation of the transition matrix of the associated Markov chain.