The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers

@article{Iglesia2020TheSM,
  title={The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers},
  author={Manuel Dom{\'i}nguez de la Iglesia and Claudia Juarez},
  journal={J. Approx. Theory},
  year={2020},
  volume={258},
  pages={105458}
}
Birth-death chains on a spider: spectral analysis and reflecting-absorbing factorization
We consider discrete-time birth-death chains on a spider, i.e. a graph consisting of N discrete half lines on the plane that are joined at the origin. This process can be identified with a
Absorbing-reflecting factorizations for birth-death chains on the integers and their Darboux transformations
Spectral analysis of bilateral birth-death processes: some new explicit examples
We consider the spectral analysis of several examples of bilateral birth-death processes and compute explicitly the spectral matrix and the corresponding orthogonal polynomials. We also use the

References

SHOWING 1-10 OF 42 REFERENCES
Stochastic LU factorizations, Darboux transformations and urn models
TLDR
By inverting the order of the factors (also known as a Darboux transformation), a new family of random walks is obtained where it is possible to state the spectral measures in terms of a Geronimus transformation.
Stochastic Darboux transformations for quasi-birth-and-death processes and urn models
Matrix Measures and Random Walks with a Block Tridiagonal Transition Matrix
TLDR
This paper derives sufficient conditions such that the blocks of the n-step block tridiagonal transition matrix of the Markov chain can be represented as integrals with respect to a matrix valued spectral measure.
LU-Factorization Versus Wiener-Hopf Factorization for Markov Chains
Our initial motivation was to understand links between Wiener-Hopf factorizations for random walks and LU-factorizations for Markov chains as interpreted by Grassman (Eur. J. Oper. Res.
Two stochastic models of a random walk in the U(n)-spherical duals of U(n + 1)
The random walk to be considered takes place in the δ-spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation δ of U(n). The transition matrix comes from the
Matrix Valued Orthogonal Polynomials Arising from Group Representation Theory and a Family of Quasi-Birth-and-Death Processes
TLDR
This gives a highly nontrivial example of a nonhomogeneous quasi-birth-and-death process for which the authors can explicitly compute its “n-step transition probability matrix” and its invariant distribution and some of these results are plotted to show the effect that choices of the parameter values have on the invariants distribution.
Rational spectral transformations and orthogonal polynomials
A decomposition theorem for infinite stochastic matrices
We prove that every infinite-state stochastic matrix P say, that is irreducible and consists of positive-recurrrent states can be represented in the form I-P=(A -I)(B-S), where A is strictly
A matrix-valued solution to Bochner's problem
We exhibit families of matrix-valued functions F(m,t), m = 0,1,2,...,t real, which are eigenfunctions of a fixed differential operator in t and of a fixed (block) tridiagonal semiinfinite matrix.
Some bivariate stochastic models arising from group representation theory
...
1
2
3
4
5
...