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ÎÒ×î½ü¶Áµ½Ò»ÆªÂÛÎÄÀïÃæÓÐÒ»¶Î£º A state is periodic if it is contained only in cycles in which the gcd of the cycle lengths is greater than one. A Markov process is irreducible if it consists of a single strongly connected component. An ergodic state is one that is aperiodic and persistent. A Markov chain is ergodic if all states are ergodic. In graph theory this corresponds to a single strongly connected component that is aperiodic. ÎÒ¶ÔͼÂÛ²»Á˽⣬ÏëÎÊϵÚÒ»¾ä£º A state is periodic if it is contained only in cycles in which the gcd of the cycle lengths is greater than one. ÖеÄthe gcd of the cycle lengthsÊÇʲôÒâ˼£¿ ȦµÄ³¤¶È£¿ Èç¹ûÊǵϰ£¬ÔõÑù¼ÆË㣿 gcdÊÇʲôÒâ˼£¿ÊÇ×î´ó¹«Ô¼ÊýµÄÒâ˼Â𣿠ΪʲôҪÓÐthe gcd of the cycle lengths Õâ¸ö¸ÅÄ лл£¡ |
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the gcd of the cycle lengths gcd - ?????, the greatest common divisor (g.c.d) ?h¡¤(cycle) ???]?o??DG V = ( , E)???????x y − ¡¤?? (a) ?? x − y¡¤?o?¦Ê??????????t(?????c)?¦Ã? ??l x − y¡¤??(trail)???] x x − ¡¤???Q???¡¤(circuit)?? (b) ??? x − y¡¤?o?¦Ê???c???F?????????Q??x − y ¡¤??(path)???h¡¤(cycle)??~???????????l?]¡¤???? http://www.stat.nuk.edu.tw/cbme/discrete/search.htm |
2Â¥2016-08-06 21:26:17
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G is strongly connected and the the GCD of the cycle lengths in G is 1. Convergence on Directed Graphs http://citeseerx.ist.psu.edu/vie ... p1&type=pdf Strongly connected component https://en.wikipedia.org/wiki/Strongly_connected_component |
3Â¥2016-08-06 21:33:09









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