Скачать или смотреть The Theoretical & Numerical Analysis for the Limiting Probability Vector - Wen Li

The Theoretical and Numerical Analysis for the Limiting Probability Vector of a Transition Probability Tensor - Wen Li - 6/13/13

In this talk, we establish theoretical analysis for a limiting probability distribution vector of a transition probability tensor P arising from a higher order Markov chain, and then propose and develop an iterative method to calculate this vector. In the model, the computation of such limiting probability distribution vector x can be formulated as a Z-eigenvalue problem associated with the eigenvalue 1 of P where all the entries of x are required to be non-negative and its summation must be equal to one. We show that if P is a transition probability tensor, then solutions of this Z-eigenvalue problem exist. With some suitable conditions of P, the limiting probability distribution vector is unique. Under the same uniqueness assumption, the linear convergence of the iterative method and perturbation analysis of the limiting probability vector can be established. Numerical examples are presented to illustrate the theoretical results.

joint work with Lu-Bin Cui and Michael Ng