Random difference equations and Renewal theory for products of random matrices
@article{Kesten1973RandomDE, title={Random difference equations and Renewal theory for products of random matrices}, author={Harry Kesten}, journal={Acta Mathematica}, year={1973}, volume={131}, pages={207-248} }
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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