A Probablistic Origin for a New Class of Bivariate Polynomials

Details A Probablistic Origin for a New Class of Bivariate Polynomials A Probablistic Origin for a New Class of Bivariate Polynomials

2008-12-19

arxiv.org/abs/0812.3879v1

SIGMA 4 (2008), 089, 18 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability

Scientific paper

10.3842/SIGMA.2008.089

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.

Affiliated with

Also associated with

No associations

Rating

A Probablistic Origin for a New Class of Bivariate Polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A Probablistic Origin for a New Class of Bivariate Polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Probablistic Origin for a New Class of Bivariate Polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-727262