Asymptotic properties of interactive markov chains

Abstract

For the stochastic version of Conlisk's interactive Markov chains, generalized to the case of infinitely many categories, we develop the “right”(Hilbert space) framework and prove stochastic and L ₂-convergence to the corresponding deterministic version under mild assumptions. Furthermore, a weak convergence result for the scaled difference between the stochastic and the deterministic allocation profiles is proved

Keywords:

• Interactive Markov chain
• infinitely many categories
• allocation profile
• Hilbert space
• convergence in probability and in L ₂
• weak convergence