Random difference equations and Renewal theory for products of random matrices

  title={Random difference equations and Renewal theory for products of random matrices},
  author={Harry Kesten},
  journal={Acta Mathematica},
  • H. Kesten
  • Published 1 December 1973
  • Mathematics
  • Acta Mathematica
where Mn and Qn are random d • d matrices respectively d-vectors and Yn also is a d-vector. Throughout we take the sequence of pairs (Mn, Q~), n >/1, independently and identically distributed. The equation (1.1) arises in various contexts. We first met a special case in a paper by Solomon, [20] sect. 4, which studies random walks in random environments. Closely related is the fact tha t if Yn(i) is the expected number of particles of type i in the nth generation of a d-type branching process in… 
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A n introduction to probability theory and it~
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