The embedding problem for Markov chains with three states

Mathematical Proceedings of the Cambridge Philosophical Society - Tập 87 Số 2 - Trang 285-294 - 1980
Halina Frydman1
1New York University

Tóm tắt

In this paper we consider the embedding problem for Markov chains with three states. A non-singular stochastic matrix P is called embeddable if there exists a two-parameter family of stochastic matricessatisfyingand such thatThough extensive characterizations of embeddable n × n stochastic matrices have been given in (l), (2), (3), (6), and further characterizations of embeddable 3 × 3 stochastic matrices in (4), they do not provide, except in the case of 2 × 2 stochastic matrices, easily applicable necessary and sufficient conditions for embeddability.

Từ khóa


Tài liệu tham khảo

10.1007/BF00533962

(4) Johansen S. and Ramsey F. L. A representation theorem for imbeddable 3 × 3 stochastic matrices (1973). Preprint no. 5, Institute of Mathematical Statistics, University of Copenhagen.

10.1007/BF00532720

10.1007/BF00533254

10.1007/BF00532721

10.1007/BF00534594

10.1017/S0305004100056152

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Thông tin xuất bản

Mathematical Proceedings of the Cambridge Philosophical Society

Tập 87 Số 2

285-294

Thông tin tác giả