TOTAL POSITIVITY AND THE EMBEDDING PROBLEM FOR MARKOV-CHAINS

被引：19
作者：
FRYDMAN, H
SINGER, B
机构：
[1] COLUMBIA UNIV,NEW YORK,NY 10027
[2] ROCKEFELLER UNIV,NEW YORK,NY 10021
来源：
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 1979年 / 86卷 / SEP期
基金：
美国国家科学基金会;
关键词：
D O I：
10.1017/S0305004100056152
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the class of transition matrices for the finite state time-inhomo-geneous birth and death processes coincides with the class of non-singular totally positive stochastic matrices. Thus we obtain a complete solution to the embedding problem for this class of Markov chains. © 1979, Cambridge Philosophical Society. All rights reserved.
引用
收藏
页码：339 / 344
页数：6
相关论文
共 9 条
[1]  
Gantmacher F.R., 1960, THEORY MATRICES, V2
[2]   SOME RESULTS ON IMBEDDING PROBLEM FOR FINITE MARKOV CHAINS [J].
JOHANSEN, S .
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1974, 8 (JUL) :345-351
[3]   CENTRAL LIMIT THEOREM FOR FINITE SEMIGROUPS AND ITS APPLICATION TO IMBEDDING PROBLEM FOR FINITE STATE MARKOV CHAINS [J].
JOHANSEN, S .
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1973, 26 (03) :171-190
[4]   BANG-BANG PROBLEM FOR STOCHASTIC MATRICES [J].
JOHANSEN, S .
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1973, 26 (03) :191-195
[5]   A CHARACTERIZATION OF BIRTH AND DEATH PROCESSES [J].
KARLIN, S ;
MCGREGOR, J .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1959, 45 (03) :375-379
[6]  
Karlin S., 1968, TOTAL POSITIVITY, VI
[7]   GEOMETRICAL ASPECTS OF THEORY OF NONHOMOGENEOUS MARKOV CHAINS [J].
KINGMAN, JFC .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1975, 77 (JAN) :171-183
[8]   New foundations for an infinitesimal calculation of matrices. [J].
Schlesinger, L .
MATHEMATISCHE ZEITSCHRIFT, 1931, 33 :33-61
[9]  
Whitney A.M., 1952, J ANAL MATH, V2, P88
1