Klaus Schiefermayr,
"Random walks with similar transition probabilities"
, in Journal of Computational and Applied Mathematics, Vol. 153, Nummer 1-2, Seite(n) 423-432, 2003, ISSN: 0377-0427
Original Titel:
Random walks with similar transition probabilities
Sprache des Titels:
Englisch
Original Kurzfassung:
We consider random walks on the nonnegative integers with a possible absorbing state at -1. Two such random walks X and Y are called k-similar if there exist constants C(i,j) such that for the n-step transition probabilities $\Pw_{ij}(n)=k^{-n}C(i,j)P_{ij}(n)$ hold. We give necessary and sufficient conditions for the k-similarity of two random walks both in terms of the parameters and in terms of the corresponding spectral measures which appear in the spectral representation of the n-step transition probabilities developed by Karlin and McGregor.