Conditions on free parameters via continued fractions enable stochastic UL/LU factorizations of infinite tridiagonal random walk matrices; Darboux transformations yield new walks whose spectral matrices are degree-one polynomial conjugations of Geronimus transforms of the original.
and Zhedanov, A., Self-similarity, spectral transformations and orthogona l and biorthogonal polynomials in self-similar systems , V.B
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The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers
Conditions on free parameters via continued fractions enable stochastic UL/LU factorizations of infinite tridiagonal random walk matrices; Darboux transformations yield new walks whose spectral matrices are degree-one polynomial conjugations of Geronimus transforms of the original.