On a q-Steady State Markov Chain Model based on Transformed Dual q-Krawtchouk Orthogonal Polynomials and its Limiting Behaviour

摘要

In this manuscript, for 0 < q < 1 we consider a q-discrete distribution based on transformed dual q-Krawtchouk orthogonal polynomials. This q-discrete distribution arises as a steady state distribution from an interesting Markov chain model. Furthermore, we study the limiting behaviour for this q-discrete distribution by proving that its standardization converges to a standardized transformation of a q-continuous Gauss distribution induced by the discrete q-Hermite of type I orthogonal polynomials. In addition, we present some numerical calculations using the computer program MAPLE indicating that the rate of convergence is quite strong.