The combinational structure of non-homogeneous Markov chains with countable states
Let P(s,t) denote a non-homogeneous continuous parameter Markov chain with countable state space E and parameter space [a,b], −∞<a<b<∞. Let R(s,t)={(i,j):Pij(s,t)>0}. It is shown in this paper that R(s,t) is reflexive, transitive, and independent of (s,t), s<t, if a certain weak homog...
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| Format: | Article |
| Language: | English |
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Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171283000320 |
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| _version_ | 1832550196868808704 |
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| author | A. Mukherjea A. Nakassis |
| author_facet | A. Mukherjea A. Nakassis |
| author_sort | A. Mukherjea |
| collection | DOAJ |
| description | Let P(s,t) denote a non-homogeneous continuous parameter Markov chain with countable state space E and parameter space [a,b], −∞<a<b<∞. Let R(s,t)={(i,j):Pij(s,t)>0}. It is shown in this paper that R(s,t) is reflexive, transitive, and independent of (s,t), s<t, if a certain weak homogeneity condition holds. It is also shown that the relation R(s,t), unlike in the finite state space case, cannot be expressed even as an infinite (countable) product of reflexive transitive relations for certain non-homogeneous chains in the case when E is infinite. |
| format | Article |
| id | doaj-art-225b588f21aa415a89b88a1e8d39b60a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-225b588f21aa415a89b88a1e8d39b60a2025-02-03T06:07:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016237138510.1155/S0161171283000320The combinational structure of non-homogeneous Markov chains with countable statesA. Mukherjea0A. Nakassis1University of So. Florida, Tampa 33620, FL., USAUniversity of So. Florida, Tampa 33620, FL., USALet P(s,t) denote a non-homogeneous continuous parameter Markov chain with countable state space E and parameter space [a,b], −∞<a<b<∞. Let R(s,t)={(i,j):Pij(s,t)>0}. It is shown in this paper that R(s,t) is reflexive, transitive, and independent of (s,t), s<t, if a certain weak homogeneity condition holds. It is also shown that the relation R(s,t), unlike in the finite state space case, cannot be expressed even as an infinite (countable) product of reflexive transitive relations for certain non-homogeneous chains in the case when E is infinite.http://dx.doi.org/10.1155/S0161171283000320non-homogeneous Markov chainsreflexive and transitive relationshomogeneity condition. |
| spellingShingle | A. Mukherjea A. Nakassis The combinational structure of non-homogeneous Markov chains with countable states International Journal of Mathematics and Mathematical Sciences non-homogeneous Markov chains reflexive and transitive relations homogeneity condition. |
| title | The combinational structure of non-homogeneous Markov chains with countable
states |
| title_full | The combinational structure of non-homogeneous Markov chains with countable
states |
| title_fullStr | The combinational structure of non-homogeneous Markov chains with countable
states |
| title_full_unstemmed | The combinational structure of non-homogeneous Markov chains with countable
states |
| title_short | The combinational structure of non-homogeneous Markov chains with countable
states |
| title_sort | combinational structure of non homogeneous markov chains with countable states |
| topic | non-homogeneous Markov chains reflexive and transitive relations homogeneity condition. |
| url | http://dx.doi.org/10.1155/S0161171283000320 |
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