{"id":1761,"date":"2016-05-10T09:52:17","date_gmt":"2016-05-10T01:52:17","guid":{"rendered":"http:\/\/systemsci.org\/jinshanw\/?p=1761"},"modified":"2017-11-17T00:17:35","modified_gmt":"2017-11-16T16:17:35","slug":"%e6%a6%82%e5%bf%b5%e7%bd%91%e7%bb%9c%e4%b8%8a%e7%9a%84%e9%ab%98%e6%95%88%e8%80%83%e8%af%95%e6%96%b9%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/www.systemsci.org\/jinshanw\/2016\/05\/10\/%e6%a6%82%e5%bf%b5%e7%bd%91%e7%bb%9c%e4%b8%8a%e7%9a%84%e9%ab%98%e6%95%88%e8%80%83%e8%af%95%e6%96%b9%e5%bc%8f\/","title":{"rendered":"\u6982\u5ff5\u7f51\u7edc\u4e0a\u7684\u9ad8\u6548\u8003\u8bd5\u65b9\u5f0f"},"content":{"rendered":"<p>\u5bf9\u4e8e\u4e00\u4e2a\u76f8\u4e92\u6ca1\u6709\u8054\u7cfb\u7684\u96c6\u5408\u4e2d\u6bcf\u4e2a\u4e2a\u4f53\u7684\u8003\u8bd5\uff0c\u8fd9\u91cc\u8003\u8bd5\u6307\u68c0\u67e5\u6bcf\u4e00\u4e2a\u662f\u4e0d\u662f\u597d\u7684\u6216\u8005\u662f\u4e0d\u662f\u88ab\u7406\u89e3\u638c\u63e1\u597d\u7684\uff0c\u6211\u4eec\u9664\u4e86\u5c1d\u8bd5\u6bcf\u4e00\u4e2a\u4e2a\u4f53\u6ca1\u6709\u66f4\u597d\u7684\u529e\u6cd5\u3002<\/p>\n<p>\u7136\u800c\uff0c\u5982\u679c\u4e2a\u4f53\u4e4b\u95f4\u5b58\u5728\u5173\u8054\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u628a\u8003\u8bd5\u548c\u63a8\u65ad\u7ed3\u5408\u8d77\u6765\uff0c\u627e\u5230\u6bd4\u5c1d\u8bd5\u6bcf\u4e00\u4e2a\u4e2a\u4f53\u66f4\u9ad8\u6548\u7684\u65b9\u6cd5\u3002\u7136\u800c\uff0c\u6709\u7684\u65f6\u5019\uff0c\u8fd9\u6837\u7684\u5173\u8054\u5c3d\u7ba1\u5b58\u5728\u4f46\u662f\u5f88\u96be\u4e8b\u5148\u77e5\u9053\u3002\u4f8b\u5982\uff0c\u5728\u8003\u67d0\u4e2a\u5b66\u751f\u7684\u4e00\u5806\u7269\u7406\u6982\u5ff5\u7684\u638c\u63e1\u7a0b\u5ea6\u7684\u65f6\u5019\uff0c\u5c3d\u7ba1\u7269\u7406\u6982\u5ff5\u4e4b\u95f4\u7684\u5173\u8054\u80af\u5b9a\u5b58\u5728\uff0c\u4f46\u662f\u5230\u5e95\u5982\u4f55\u5173\u8054\uff0c\u9700\u8981\u901a\u8fc7\u68c0\u6d4b\u8fd9\u4e2a\u5b66\u751f\u540c\u65f6\u638c\u63e1\u54ea\u4e00\u4e9b\uff0c\u624d\u77e5\u9053\u3002\u7136\u800c\uff0c\u6211\u4eec\u6b63\u597d\u60f3\u907f\u5f00\u8fd9\u6837\u7684\u7a77\u4e3e\u6cd5\u68c0\u6d4b\u3002\u56e0\u6b64\uff0c\u8fd9\u662f\u4e00\u4e2a\u76f8\u4e92\u4f9d\u8d56\u7684\u96be\u9898\u3002\u90a3\u6709\u6ca1\u6709\u4e00\u4e9b\u53ef\u80fd\u5177\u6709\u4ee3\u8868\u6027\u7684\u5173\u8054\u5462\uff0c\u5c3d\u7ba1\u8fd9\u6837\u7684\u5173\u8054\u5728\u4e0d\u540c\u7684\u88ab\u8bd5\u8eab\u4e0a\u4e0d\u4e00\u5b9a\u8868\u73b0\u4e00\u81f4\uff0c\u4ec5\u4ec5\u8868\u73b0\u4e3a\u67d0\u79cd\u5e73\u5747\u610f\u4e49\u4e0a\u7684\u5173\u8054\uff1f\u5982\u679c\u6709\uff0c\u8fd9\u6837\u7684\u5173\u8054\uff0c\u80fd\u4e0d\u80fd\u4e0d\u4f9d\u8d56\u4e8e\u68c0\u6d4b\u5f97\u5230\u5462\uff1f\u5f97\u5230\u8fd9\u6837\u7684\u5173\u8054\u4e4b\u540e\uff0c\u53c8\u5982\u4f55\u548c\u63a8\u65ad\u7ed3\u5408\u8d77\u6765\uff0c\u5e2e\u52a9\u5b9e\u73b0\u66f4\u9ad8\u6548\u7684\u8003\u8bd5\u5462\uff1f\u8fd9\u4e2a\u5e16\u5b50\u5c1d\u8bd5\u56de\u7b54\u8fd9\u4e9b\u95ee\u9898\uff0c\u6216\u8005\u8bf4\uff0c\u7ed9\u51fa\u4e00\u4e2a\u56de\u7b54\u8fd9\u4e9b\u95ee\u9898\u7684\u6846\u67b6\u3002<\/p>\n<p>\u6211\u4eec\u8ba4\u4e3a\uff0c\u6982\u5ff5\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\uff0c\u53ef\u4ee5\u505a\u4e3a\u5173\u8054\u7684\u5ba2\u89c2\u8868\u73b0\u3002\u4ee5\u6c49\u5b57\u4e3a\u4f8b\uff0c\u6c49\u5b57\u4e4b\u95f4\u901a\u8fc7\u7ed3\u6784\u5173\u7cfb\u76f8\u4e92\u8054\u7cfb\uff0c\u8fd9\u4e00\u70b9\u662f\u5ba2\u89c2\u7684\uff08\u5c3d\u7ba1\u7e41\u4f53\u5b57\u548c\u7b80\u4f53\u5b57\u5728\u6c49\u5b57\u4e4b\u95f4\u662f\u5982\u4f55\u4ece\u7ed3\u6784\u4e0a\u8054\u7cfb\u8d77\u6765\u7684\u8fd9\u4e00\u70b9\u4e0a\u4e0d\u4e00\u6837\u3002\u5148\u8003\u8651\u4f8b\u5982\u4ec5\u4ec5\u7b80\u4f53\u5b57\uff09\u3002\u4f8b\u5982\uff1a\u6728\u2014\u2014\u6797\u2014\u2014\u68ee\uff0c\u4eba\u2014\u2014\u4ece\u2014\u2014\u4f17\uff0c\u6c34\u2014\u2014\u51b0\u2014\u2014\u6dfc\uff0c\uff08\u6728\uff0c\u4e00\uff09\u2014\u2014\u672c\uff0c\uff08\u4eba\uff0c\u672c\uff09\u2014\u2014\u4f53\u3002\u5f53\u7136\uff0c\u8fd9\u4e2a\u5ba2\u89c2\u7684\u7ed3\u6784\u8054\u7cfb\u662f\u5426\u5c31\u80fd\u4ee3\u8868\u903b\u8f91\u8054\u7cfb\uff0c\u662f\u6709\u5f85\u8ba8\u8bba\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u6c49\u5b57\u96c6\u5408\u4e0a\uff0c\u5b58\u5728\u7740\u4e00\u4e2a\u903b\u8f91\u5173\u7cfb\u7f51\u7edc\uff0c\u7f51\u7edc\u7684\u6bcf\u4e00\u6761\u8fb9\u4ee3\u8868\u4e0a\u9762\u4e3e\u4f8b\u4e2d\u7684\u4e00\u4e2a\u5b57\\(i\\)\u6210\u4e3a\u53e6\u4e00\u4e2a\u5b57\\(j\\)\u7684\u4e00\u90e8\u5206\u8fd9\u6837\u7684\u7ed3\u6784\u5173\u7cfb\\(A=\\left(a^{i}_{j}\\right)_{N\\times N}\\)\u3002\u8fd9\u4e2a\u7ed3\u6784\u5173\u7cfb\u4e0a\u9762\u53e0\u52a0\u4e86\u4e00\u5c42\u903b\u8f91\u5173\u7cfb\u3002\u8fd9\u4e2a\u903b\u8f91\u5173\u7cfb\uff0c\u6211\u4eec\u901a\u8fc7\u4e0b\u9762\u7684\u51e0\u4e2a\u6743\u91cd\u2014\u2014\u5df2\u77e5\u8ba4\u8bc6\u4e00\u4e2a\u5b57\uff0c\u63a8\u65ad\u53e6\u5916\u4e00\u4e2a\u5b57\u4e5f\u8ba4\u8bc6\u7684\u6761\u4ef6\u6982\u7387\u2014\u2014\u6765\u8868\u8fbe\u3002\u4efb\u4f55\u4e00\u4e2a\u65f6\u5019\u6bcf\u4e00\u4e2a\u5b57\\(j\\)\u7684\u68c0\u6d4b\u72b6\u6001\u8bb0\u4e3a\uff08\\(c_{j}k_{j}=\\left\\{11, 1-1, 01, 00, 0-1\\right\\}\\)\uff09\u5206\u522b\u4ee3\u8868\u68c0\u6d4b\u8fc7\u8ba4\u8bc6\uff0c\u68c0\u6d4b\u8fc7\u4e0d\u8ba4\u8bc6\uff0c\u6ca1\u6709\u68c0\u6d4b\u8fc7\u63a8\u65ad\u8ba4\u8bc6\uff0c\u6ca1\u6709\u68c0\u6d4b\u8fc7\u63a8\u65ad\u72b6\u6001\u4e3a\u672a\u77e5\uff0c\u6ca1\u6709\u68c0\u6d4b\u8fc7\u63a8\u65ad\u4e0d\u8ba4\u8bc6\uff0c\u8fd9\u4e94\u4e2a\u72b6\u6001\u3002\u6ce8\u610f\uff0c\u51e1\u662f\u68c0\u6d4b\u8fc7\u7684\u5b57\u7684\u72b6\u6001\u5c31\u4e0d\u518d\u7528\u4e0b\u9762\u7684\u6761\u4ef6\u6982\u7387\u6765\u66f4\u65b0\u4e86\u3002<\/p>\n<ol>\n<li>\u8ba4\u8bc6\u4e0a\u5c42\u5b57\\(i\\)\uff0c\u63a8\u65ad\u4e0b\u5c42\u5b57\u8ba4\u8bc6\\(j\\)\u7684\u6982\u7387\uff0c\\(\\omega^{i, \\left(1\\downarrow\\right)}_{j} \\)\uff0c\u548c\u7ed3\u6784\u77e9\u9635\u7684\u5143\u7d20\\(a^{j}_{i}\\)\u6709\u5173\u3002\u539f\u5219\u4e0a\u53ef\u4ee5\u4e0d\u9075\u5faa\u7ed3\u6784\u77e9\u9635\uff0c\u6765\u81ea\u4e8e\u5176\u4ed6\u5b9e\u8bc1\u5173\u7cfb\u3002\u505a\u4e3a\u4e00\u4e2a\u7b80\u5316\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\\(\\omega^{i, \\left(1\\downarrow\\right)}_{j} =a^{j}_{i}=1\\)\u3002<\/li>\n<li>\u8ba4\u8bc6\u4e0b\u5c42\u5b57\\(i\\)\uff0c\u63a8\u65ad\u4e0a\u5c42\u5b57\u8ba4\u8bc6\\(j\\)\u7684\u6982\u7387\uff0c\\(\\omega^{i, \\left(1\\uparrow\\right)}_{j} \\)\uff0c\u548c\u7ed3\u6784\u77e9\u9635\u7684\u5143\u7d20\\(a^{i}_{j}\\)\u6709\u5173\u3002\u539f\u5219\u4e0a\u53ef\u4ee5\u4e0d\u9075\u5faa\u7ed3\u6784\u77e9\u9635\uff0c\u6765\u81ea\u4e8e\u5176\u4ed6\u5b9e\u8bc1\u5173\u7cfb\u3002\u505a\u4e3a\u4e00\u4e2a\u7b80\u5316\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\\(\\omega^{i, \\left(1\\uparrow\\right)}_{j} = 0\\)\u3002<\/li>\n<li>\u4e0d\u8ba4\u8bc6\u4e0a\u5c42\u5b57\\(i\\)\uff0c\u63a8\u65ad\u4e0b\u5c42\u5b57\u4e0d\u8ba4\u8bc6\\(j\\)\u7684\u6982\u7387\uff0c\\(\\omega^{i, \\left(-1\\downarrow\\right)}_{j} \\)\uff0c\u548c\u7ed3\u6784\u77e9\u9635\u7684\u5143\u7d20\\(a^{j}_{i}\\)\u6709\u5173\u3002\u539f\u5219\u4e0a\u53ef\u4ee5\u4e0d\u9075\u5faa\u7ed3\u6784\u77e9\u9635\uff0c\u6765\u81ea\u4e8e\u5176\u4ed6\u5b9e\u8bc1\u5173\u7cfb\u3002\u505a\u4e3a\u4e00\u4e2a\u7b80\u5316\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\\(\\omega^{i, \\left(-1\\downarrow\\right)}_{j} =0\\)\u3002<\/li>\n<li>\u4e0d\u8ba4\u8bc6\u4e0b\u5c42\u5b57\\(i\\)\uff0c\u63a8\u65ad\u4e0a\u5c42\u5b57\u4e0d\u8ba4\u8bc6\\(j\\)\u7684\u6982\u7387\uff0c\\(\\omega^{i, \\left(-1\\uparrow\\right)}_{j} \\)\uff0c\u548c\u7ed3\u6784\u77e9\u9635\u7684\u5143\u7d20\\(a^{i}_{j}\\)\u6709\u5173\u3002\u539f\u5219\u4e0a\u53ef\u4ee5\u4e0d\u9075\u5faa\u7ed3\u6784\u77e9\u9635\uff0c\u6765\u81ea\u4e8e\u5176\u4ed6\u5b9e\u8bc1\u5173\u7cfb\u3002\u505a\u4e3a\u4e00\u4e2a\u7b80\u5316\u6a21\u578b\uff0c\u6211\u4eec\u53ef\u4ee5\u5047\u8bbe\\(\\omega^{i, \\left(-1\\uparrow\\right)}_{j} =a^{i}_{j}=1\\)\u3002<\/li>\n<\/ol>\n<p>\u5728\u8fd9\u91cc\uff0c\u7b80\u5316\u6a21\u578b\u7684\u7406\u5ff5\u662f\u8ba4\u8bc6\u66f4\u590d\u6742\u7684\u610f\u5473\u7740\u8ba4\u8bc6\u7b80\u5355\u7684\u5b50\u7ed3\u6784\uff0c\u4e0d\u8ba4\u8bc6\u66f4\u7b80\u5355\u7684\u5b50\u7ed3\u6784\u5219\u66f4\u590d\u6742\u7684\u5408\u6210\u5b57\u80af\u5b9a\u4e0d\u8ba4\u8bc6\u3002\u6ce8\u610f\uff0c\u8fd9\u4e2a\u662f\u5bf9\u539f\u59cb\u95ee\u9898\u7684\u4e00\u4e2a\u6781\u5927\u7684\u7b80\u5316\u3002<\/p>\n<p>\u73b0\u5728\uff0c\u6211\u4eec\u6709\u4e86\u4e00\u4e2a\u7ed3\u6784\u7f51\u7edc\\(A\\)\uff0c\u56db\u4e2a\u8fd9\u4e2a\u7f51\u7edc\u4e0a\u7684\u903b\u8f91\u5173\u7cfb\\(\\Omega^{\\left(1\\downarrow\\right)}, \\Omega^{\\left(1\\uparrow\\right)}, \\Omega^{\\left(-1\\downarrow\\right)}, \\Omega^{\\left(-1\\uparrow\\right)}\\)\u3002\u6bcf\u4e00\u4e2a\u9876\u70b9\u6709\u4e94\u4e2a\u72b6\u6001\\(c_{j}k_{j}=\\left\\{11, 1-1, 01, 00, 0-1\\right\\}\\)\u3002\u521d\u59cb\u65f6\u523b\uff0c\u6240\u6709\u9876\u70b9\u7684\u72b6\u6001\u90fd\u662f\u672a\u68c0\u6d4b\u4e5f\u65e0\u4ece\u63a8\u65ad\\(p\\left(0_{j}0_{j},t\\right)=1\\)\u3002\u5728\u68c0\u6d4b\u8fc7\u7a0b\u4e2d\uff0c\u5bf9\u4e8e\u786e\u5b9a\u6027\u6a21\u578b\uff0c\u4efb\u610f\u4e00\u4e2a\u9876\u70b9\u7684\u72b6\u6001\u4e5f\u662f\u4ee5\u4e0a\u4e94\u4e2a\u72b6\u6001\u4e4b\u4e00\u3002\u5bf9\u4e8e\u968f\u673a\u6a21\u578b\uff0c\u6211\u4eec\u6709\u9876\u70b9\u5904\u4e8e\u72b6\u6001\\(c_{j}k_{j}\\)\u7684\u51e0\u7387\u4e3a<br \/>\n\\[p\\left(c_{j}k_{j}, t\\right).\\]<br \/>\n\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u9876\u70b9\\(j\\)\uff0c\u8fd9\u4e9b\u6982\u7387\u5bf9\\(ck\\)\u7684\u53d6\u548c\u5f52\u4e00\u3002\u540c\u65f6\uff0c\u524d\u9762\u4e24\u4e2a\u72b6\u6001\u7684\u53d6\u503c\u53ea\u80fd\u662f\\(0,1\\)\uff0c\u4e5f\u5c31\u662f\uff0c<br \/>\n\\[p\\left(1_{j}k_{j}, t\\right) = 1,0.\\]<\/p>\n<p>\u7531\u4e8e\u7531\u8fd9\u4e9b\u6982\u7387\u7684\u7279\u6b8a\u53d6\u503c\uff0c\u4e3a\u4e86\u66f4\u597d\u5730\u63cf\u8ff0\u540e\u9762\u7684\u52a8\u529b\u5b66\u8fc7\u7a0b\uff0c\u6211\u4eec\u5b9a\u4e49\u4e00\u5957\u65b0\u7684\u72b6\u6001\u53d8\u91cf\u3002\u5b9a\u4e49\u4e00\u4e2a\u79bb\u6563\u53d8\u91cf\\(\\xi_{j}\\)\u548c\u4e24\u4e2a\u8fde\u7eed\u53d8\u91cf\\(\\eta^{\\left(1\\right)}_{j}, \\eta^{\\left(-1\\right)}_{j}\\)\u66f4\u52a0\u5408\u9002\u3002\u63cf\u8ff0\u53d8\u91cf\u91c7\u7528\\(\\xi_{j}=\\pm 1, 0\\), \\(\\eta^{\\left(\\pm1\\right)}_{j} \\in \\left[0, \\infty\\right]\\)\u3002\\(\\xi_{j}=1\\)\u8868\u793a\\(1_{j}1_{j}\\)\u6001\uff0c\\(\\xi_{j}=-1\\)\u8868\u793a\\(1_{j}-1_{j}\\)\u6001\uff0c\\(\\xi_{j}=0\\)\u7684\u65f6\u5019\uff0c\u770b\\(\\eta^{\\left(\\pm1\\right)}_{j}\\)\u3002\u8fd9\u4e2a\u65f6\u5019\u63a8\u65ad\u72b6\u6001\u7684\u51e0\u7387\u5206\u522b\u662f<br \/>\n\\begin{align}<br \/>\nq^{\\left(01\\right)}=p\\left(0_{j}1_{j},t\\right) = \\frac{\\eta^{\\left(1\\right)}_{j} \\left(t\\right) &#8211; \\eta^{\\left(-1\\right)}_{j} \\left(t\\right)}{\\eta^{\\left(1\\right)}_{j} \\left(t\\right) + \\eta^{\\left(-1\\right)}_{j} \\left(t\\right)}\\theta\\left(\\eta^{\\left(1\\right)}_{j} \\left(t\\right) &#8211; \\eta^{\\left(-1\\right)}_{j} \\left(t\\right)\\right) \\notag \\\\<br \/>\np\\left(0_{j}0_{j},t\\right) = 1-\\frac{\\left|\\eta^{\\left(1\\right)}_{j} \\left(t\\right) &#8211; \\eta^{\\left(-1\\right)}_{j} \\left(t\\right)\\right|}{\\eta^{\\left(1\\right)}_{j} \\left(t\\right) + \\eta^{\\left(-1\\right)}_{j} \\left(t\\right)} \\notag \\\\<br \/>\nq^{\\left(0-1\\right)}=p\\left(0_{j}-1_{j},t\\right) = \\frac{\\eta^{\\left(-1\\right)}_{j} \\left(t\\right) &#8211; \\eta^{\\left(1\\right)}_{j} \\left(t\\right)}{\\eta^{\\left(1\\right)}_{j} \\left(t\\right) + \\eta^{\\left(-1\\right)}_{j} \\left(t\\right)}\\theta\\left(\\eta^{\\left(-1\\right)}_{j} \\left(t\\right) &#8211; \\eta^{\\left(1\\right)}_{j} \\left(t\\right)\\right)<br \/>\n\\end{align}<br \/>\n\u6309\u7167\u8fd9\u6837\u7684\u72b6\u6001\u6807\u8bb0\uff0c\u6211\u4eec\u53d6\u6bcf\u4e00\u4e2a\u9876\u70b9\u7684\u72b6\u6001\u53d8\u91cf\u4e3a\uff1a\\(\\xi_{j}, \\eta^{\\left(1\\right)}_{j}, \\eta^{\\left(-1\\right)}_{j}\\)\u3002\u5b9e\u9645\u4e0a\uff0c\u6211\u4eec\u770b\u5230\uff0c\u7cfb\u7edf\u7684\u72b6\u6001\u5f53\\(\\xi_{j}=\\pm 1\\)\u7684\u65f6\u5019\u5f88\u7b80\u5355\uff08\u5c31\u662f\\(1_{j}1_{j},1_{j}-1_{j}\\)\u6001\uff09\u3002\u5f53\\(\\xi_{j}=0\\)\u7684\u65f6\u5019\uff0c\u7cfb\u7edf\u5728\u72b6\u6001\\(c_{j}k_{j}=\\left\\{01, 00, 0-1\\right\\}\\)\u5b50\u7a7a\u95f4\u4e0a\u7684\u6982\u7387\u77e2\u91cf\u662f\uff0c<br \/>\n\\[\\left[q^{\\left(01\\right)}, 1-q^{\\left(01\\right)}, 0\\right]^{T},\\]<br \/>\n\u6216\u8005<br \/>\n\\[\\left[0, 1-q^{\\left(0-1\\right)}, q^{\\left(0-1\\right)}\\right]^{T}.\\]<br \/>\n\u4e5f\u5c31\u662f\u8bf4\uff0c\u72b6\u6001\u53d8\u91cf\\(\\xi_{j}\\)\u548c\\(\\eta^{\\left(1\\right)}_{j}, \\eta^{\\left(-1\\right)}_{j}\\)\u4ecd\u7136\u4e0d\u662f\u53cd\u6620\u7cfb\u7edf\u72b6\u6001\u7684\u6700\u7b80\u5355\u7684\u8868\u8fbe\u65b9\u5f0f\uff08\u6709\u4fe1\u606f\u6ca1\u6709\u88ab\u7528\u5230\uff09\u3002\u4e0d\u8fc7\uff0c\u6682\u65f6\uff0c\u6211\u4eec\u5c31\u4ee5\u8fd9\u5957\u72b6\u6001\u53d8\u91cf\u4e3a\u51c6\uff1a<br \/>\n\\[\\xi_{j},\\eta^{\\left(\\pm 1\\right)}_{j} \\Longleftrightarrow p\\left(c_{j}k_{j}\\right). \\]<\/p>\n<p>\u73b0\u5728\uff0c\u6211\u4eec\u5df2\u7ecf\u6e05\u695a\u4e86\u7cfb\u7edf\u72b6\u6001\u7684\u63cf\u8ff0\\(P\\)\uff08\u6bcf\u4e00\u4e2a\u5b57\u90fd\u6709\u4e00\u4e2a\u72b6\u6001\u5206\u5e03\u51fd\u6570\uff0c\u6574\u4f53\u72b6\u6001\u6784\u6210\u4e00\u4e2a\u5206\u5e03\u51fd\u6570\u5927\u77e2\u91cf\u3002\u8fd9\u4e2a\u77e2\u91cf\u7684\u5177\u4f53\u5199\u6cd5\u53ef\u4ee5\u91c7\u7528\u76f4\u79ef\u6216\u8005\u76f4\u548c\uff0c\u518d\u8bf4\uff0c\u73b0\u5728\u7528\u4e0d\u7740\uff09\u548c\u521d\u59cb\u6761\u4ef6\\(P\\left(0\\right)\\)\uff0c\u6211\u4eec\u6765\u6784\u9020\u4e00\u4e2a\u52a8\u529b\u5b66\u8fc7\u7a0b\\(P\\left(t-1\\right)\\rightarrow P\\left(t\\right)\\)\u3002\u5c06\u6765\uff0c\u6211\u4eec\u8981\u8ba8\u8bba\u8fd9\u6837\u7684\u95ee\u9898\uff1a\u5728\u7ed9\u5b9a\u6210\u672c\u7684\u60c5\u51b5\u4e0b\uff0c\u5982\u4f55\u8ba9\u7cfb\u7edf\u5c3d\u53ef\u80fd\u5730\u8fbe\u5230\u67d0\u4e2a\u9884\u671f\u72b6\u6001\uff0c\u6216\u8005\u8fbe\u5230\u67d0\u4e2a\u9884\u671f\u72b6\u6001\u6240\u9700\u8981\u7684\u6700\u5c11\u7684\u6210\u672c\u3002<\/p>\n<p>\u6211\u4eec\u5148\u8ba8\u8bba\u52a8\u529b\u5b66\u8fc7\u7a0b\u3002\u6bcf\u4e00\u6b65\uff08\u8bb0\u4e3a\\(t\\)\u65f6\u523b\uff09\uff0c\u6211\u4eec\u9009\u62e9\u4e00\u4e2a\u6c49\u5b57\\(i\\)\u6765\u68c0\u6d4b\u662f\u5426\u88ab\u8bd5\u8ba4\u8bc6\u3002<\/p>\n<ol>\n<li>\u5982\u679c\u8ba4\u8bc6\uff08\u4e0d\u8ba4\u8bc6\uff09\uff0c\u5219\u66f4\u65b0\u8fd9\u4e2a\u5b57\u7684\u72b6\u6001\u4e3a\\(\\xi_{i}=1\\)\uff08\\(\\xi_{i}=-1\\)\uff09\u3002<\/li>\n<li>\u7136\u540e\uff0c\u8003\u5bdf\u8fd9\u4e2a\u5b57\u7684\u4e00\u7ea7\u8fd1\u90bb\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u4e00\u7ea7\u8fd1\u90bb\\(j\\)\u6309\u7167\u5982\u4e0b\u65b9\u5f0f\u66f4\u65b0\u5176\u72b6\u6001\uff1a<\/li>\n<ol>\n<li>\u5982\u679c\\(\\xi_{j}=\\pm 1\\)\uff0c\u505c\u6b62\u66f4\u65b0\\(j\\)\u7684\u72b6\u6001<\/li>\n<li>\u5426\u5219\uff08\u4e5f\u5c31\u662f\\(\\xi_{j}=0\\)\u7684\u65f6\u5019\uff09\uff0c\u53d6\\(\\eta^{\\left(\\pm 1\\right)}_{j}\\)\u7684\u5f53\u524d\u503c\\(\\eta^{\\left(\\pm 1\\right)}_{j}\\left(t-1\\right)\\)\uff0c\u6309\u7167\\(i\\)\u7684\u72b6\u6001\u6765\u66f4\u65b0\\(j\\)\u7684\u72b6\u6001<\/li>\n<ol>\n<li>\u5982\u679c\\(\\xi_{i}=1\\)\uff0c\u5219<\/li>\n<p>\\begin{align}<br \/>\n\\eta^{\\left(1\\right)}_{j}\\left(t\\right) = \\eta^{\\left(1\\right)}_{j}\\left(t-1\\right) + \\omega^{\\left(1\\uparrow\\right),i}_{j}+ \\omega^{\\left(1\\downarrow\\right),i}_{j}<br \/>\n\\end{align}<\/p>\n<li>\u5982\u679c\\(\\xi_{i}=-1\\)\uff0c\u5219<\/li>\n<p>\\begin{align}<br \/>\n\\eta^{\\left(-1\\right)}_{j}\\left(t\\right) = \\eta^{\\left(-1\\right)}_{j}\\left(t-1\\right) + \\omega^{\\left(-1\\uparrow\\right),i}_{j}+ \\omega^{\\left(-1\\downarrow\\right),i}_{j}<br \/>\n\\end{align}\n        <\/ol>\n<\/ol>\n<\/ol>\n<p>\u628a\u4ee5\u4e0a\u7684\u8fc7\u7a0b\u5408\u8d77\u6765\uff0c\u4e5f\u5c31\u662f<\/p>\n<ol>\n<li>\u5bf9\u5b57\\(i\\)\u505a\u68c0\u6d4b\u4ee5\u540e\uff0c\u5982\u679c\u8ba4\u8bc6\uff08\u4e0d\u8ba4\u8bc6\uff09\uff0c\u5219\u66f4\u65b0\u8fd9\u4e2a\u5b57\u7684\u72b6\u6001\u4e3a\\(\\xi_{i}=1\\)\uff08\\(\\xi_{i}=-1\\)\uff09\u3002<\/li>\n<li>\u7136\u540e\uff0c\u8003\u5bdf\\(i\\)\u8fd9\u4e2a\u5b57\u7684\u4e00\u7ea7\u8fd1\u90bb\u3002\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u4e00\u7ea7\u8fd1\u90bb\\(j\\)\u6309\u7167\u5982\u4e0b\u65b9\u5f0f\u66f4\u65b0\u5176\u72b6\u6001\uff1a<\/li>\n<p>\\begin{align}<br \/>\n\\eta^{\\left(\\xi_{i}\\right)}_{j}\\left(t\\right) =  \\eta^{\\left(\\xi_{i}\\right)}_{j}\\left(t-1\\right) + \\left(1+\\xi_{j}\\right)\\left(1-\\xi_{j}\\right)\\left[\\left(\\omega^{\\left(\\xi_{i}\\uparrow\\right),i}_{j}+ \\omega^{\\left(\\xi_{i}\\downarrow\\right),i}_{j}\\right)\\right]<br \/>\n\\end{align}\n<\/ol>\n<p>\u5fc5\u8981\u7684\u65f6\u5019\u53ef\u4ee5\u8ba1\u7b97\u6982\u7387\\(p\\left(c_{j}k_{j},t\\right)\\) \u3002\u8fd9\u4e2a\u8fc7\u7a0b\u63cf\u8ff0\u4e86\u6d4b\u5f97\u4e00\u4e2a\u65b0\u7684\u5b57\u662f\u5426\u8ba4\u8bc6\u4ee5\u540e\u5728\u6574\u4e2a\u7f51\u7edc\u4e0a\u7684\u4f20\u64ad\u3002\u4e0a\u9762\u7684\u8fc7\u7a0b\u4ec5\u4ec5\u8003\u8651\u4f20\u64ad\u4e00\u6b65\uff0c\u4e5f\u5c31\\(i\\)\u7684\u90bb\u5c45\u4eec\u3002\u4e00\u4e2a\u66f4\u52a0\u590d\u6742\u7684\u6a21\u578b\u53ef\u4ee5\u8003\u8651\u591a\u6b65\u4f20\u64ad\uff1a\u4e5f\u5c31\u662f\u8ba1\u7b97\u4e00\u7ea7\u8fd1\u90bb\u7684\u72b6\u6001\u6982\u7387\u77e2\u91cf\u4e4b\u540e\uff0c\u62ff\u7740\u8fd9\u4e2a\u66f4\u65b0\u4e86\u7684\u77e2\u91cf\uff0c\u518d\u53bb\u8ba1\u7b97\u4e8c\u7ea7\u8fd1\u90bb\u7684\u72b6\u6001\u77e2\u91cf\u3002<\/p>\n<p>\u518d\u6765\u8ba8\u8bba\u76ee\u6807\u3002<\/p>\n<p>\u73b0\u5728\uff0c\u6211\u4eec\u5e0c\u671b\u5f97\u5230\u4e00\u4e2a\uff08\u6709\u987a\u5e8f\u7684\uff09\u68c0\u6d4b\u7684\u96c6\u5408\uff0c\u6216\u8005\u4e00\u4e2a\u6309\u7167\u68c0\u6d4b\u7ed3\u679c\u5b9e\u65f6\u81ea\u9002\u5e94\u751f\u6210\u68c0\u6d4b\u987a\u5e8f\u7684\u7b97\u6cd5\u3002\u8fd9\u4e2a\u7b97\u6cd5\u6216\u8005\u96c6\u5408\u8981\u505a\u5230\u4ee5\u4e0b\u4e24\u4e2a\u76ee\u6807\u4e2d\u7684\u4e00\u4e2a\u3002<\/p>\n<ol>\n<li>\u7ed9\u5b9a\u68c0\u6d4b\u6210\u672c\\(C=\\sum_{j}c_{j}\\)\u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u5927\u5316\u4ee5\u4e0b\u7684\u76ee\u6807\u51fd\u6570\u7684\u68c0\u6d4b\u987a\u5e8f\u662f\u4ec0\u4e48\uff1a<br \/>\n\\[K=\\sum_{j,c_{j}} \\left|p\\left(c_{j}1_{j}; C\\right) &#8211; p\\left(c_{j}-1_{j}; C\\right)\\right|\\]<br \/>\n\u6700\u540e\u7684\u53c2\u6570\\(C\\)\u8868\u793a\\(C\\)\u65f6\u523b\uff0c\u5982\u679c\u8bb0\u6bcf\u4e00\u6b21\u68c0\u6d4b\u65b0\u7684\u6c49\u5b57\u7b97\u4e00\u4e2a\u65f6\u95f4\u6b65\u7684\u8bdd\u3002<\/li>\n<li>\u6216\u8005\u671f\u671b\u8fbe\u5230\u67d0\u4e2a\u7279\u5b9a\u7684\\(K_{aim}\\)\uff0c\u6700\u5c0f\u7684\\(C\\)\u662f\u591a\u5c11\uff0c\u5b9e\u73b0\u8fd9\u6837\u7684\u6700\u5c0f\\(C\\)\u7684\u68c0\u6d4b\u987a\u5e8f\u662f\u4ec0\u4e48\u3002<\/li>\n<\/ol>\n<p>\u7528\u65b0\u7684\u72b6\u6001\u8bb0\u53f7\uff0c\u76ee\u6807\u51fd\u6570\u53ef\u4ee5\u5199\u505a<br \/>\n\\[K=\\sum_{j} \\left(\\frac{\\left|\\eta^{\\left(1\\right)}_{j}-\\eta^{\\left(-1\\right)}_{j}\\right|}{\\eta^{\\left(1\\right)}_{j}+\\eta^{\\left(-1\\right)}_{j}}\\right).\\]<br \/>\n\u6ce8\u610f\uff0c\u5f53\\(\\xi_{j}=\\pm 1\\)\u7684\u65f6\u5019\uff0c\u6211\u4eec\u5f3a\u884c\u66f4\u65b0\u4e86\\(\\eta^{\\pm 1}_{j}\\)\u6765\u628a\u524d\u8005\u7684\u4fe1\u606f\u8f6c\u5165\u5230\u540e\u8005\u4e4b\u4e2d\uff0c\u4e8e\u662f\uff0c\u8fd9\u4e2a\u76ee\u6807\u51fd\u6570\u7684\u5b9a\u4e49\u770b\u8d77\u6765\u7b80\u5355\u4e00\u4e9b\u3002<\/p>\n<p>\u5728\u8fd9\u4e2a\u8bed\u8a00\u4e0b\uff0c\u95ee\u9898\u6210\u4e86\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u68c0\u6d4b\u987a\u5e8f\uff0c\u6216\u8005\u4e00\u4e2a\u68c0\u6d4b\u987a\u5e8f\u7684\u81ea\u9002\u5e94\u7b97\u6cd5\uff0c\u6574\u4e2a\u95ee\u9898\u5c31\u662f\u4e00\u4e2aMarkov\u94fe\uff0c\u7136\u540e\u8fd9\u4e2a\u94fe\u9700\u8981\u6ee1\u8db3\u4e0a\u9762\u4e24\u4e2a\u76ee\u6807\u4e4b\u4e00\u7684\u8bdd\uff0c\u600e\u4e48\u529e\uff1f<\/p>\n<p>\u5f53\u7136\uff0c\u4e0d\u7528\u8fd9\u4e2a\u6574\u4f53\u7cfb\u7edf\u72b6\u6001\u7684\u8bed\u8a00\uff0c\u5c31\u662f\u95ee\u4ec0\u4e48\u6837\u7684\u96c6\u5408\u7684\u9009\u62e9\u6216\u8005\u987a\u5e8f\u7684\u9009\u62e9\uff0c\u6216\u8005\u751f\u6210\u987a\u5e8f\u7684\u7b97\u6cd5\u7684\u9009\u62e9\uff0c\u80fd\u591f\u4fdd\u8bc1\u7528\u6700\u5c11\u7684\u68c0\u6d4b\u6b21\u6570\uff0c\u4e86\u89e3\u6700\u591a\u7684\u6c49\u5b57\u662f\u5426\u88ab\u8ba4\u5f97\u3002<\/p>\n<p>\u5bf9\u4e8e\u7b80\u5316\u6a21\u578b\u2014\u2014\u5173\u7cfb\u77e9\u9635\\(\\Omega\\)\u7684\u5143\u7d20\u5c31\u662f\\(0,1\\)\u7684\u60c5\u51b5\uff0c\u76f8\u5f53\u4e8e\u8ba8\u8bba\u4e00\u4e2a\u53cc\u6001\u7684\u652f\u914d\u96c6\u95ee\u9898\uff1a\u4e24\u4e2a\u72b6\u6001\u53ef\u4ee5\u5728\u6709\u5411\u65e0\u6743\u7f51\u7edc\u4e0a\u4f20\u64ad\u4e00\u6b65\uff0c\u95ee\u67d0\u79cd\u610f\u4e49\u4e0a\u6700\u5c0f\u7684\u9700\u8981\u68c0\u6d4b\u51fa\u6765\u786e\u5b9a\u72b6\u6001\u7684\u96c6\u5408\u662f\u4ec0\u4e48\u3002\u5f53\u7136\uff0c\u53ef\u4ee5\u9884\u89c1\uff0c\u8fd9\u4e2a\u6700\u5c0f\u96c6\u5408\u4f1a\u548c\u6bcf\u4e00\u6b21\u68c0\u6d4b\u7684\u7ed3\u679c\u6709\u5173\u7cfb\uff1a\u6781\u7aef\u60c5\u51b5\uff0c\u5047\u8bbe\u6bcf\u6b21\u68c0\u6d4b\u7ed3\u679c\u90fd\u662f\\(1\\)\u7684\u6700\u5c0f\u96c6\u5408\uff0c\u548c\u6bcf\u6b21\u68c0\u6d4b\u7ed3\u679c\u90fd\u662f\\(-1\\)\u7684\uff0c\u80af\u5b9a\u662f\u4e0d\u4e00\u6837\u7684\u3002\u56e0\u6b64\uff0c\u8fd9\u4e2a\u95ee\u9898\uff0c\u4e0d\u662f\u5355\u7eaf\u7684\u4e24\u4e2a\u5355\u72b6\u6001\u652f\u914d\u96c6\u95ee\u9898\u7684\u76f8\u52a0\u3002<\/p>\n<p>\u6362\u4e00\u4e2a\u89d2\u5ea6\u6765\u770b\uff0c\u5728\u7b80\u5316\u6a21\u578b\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u4e2a\u95ee\u9898\u662f\u53cc\u5173\u7cfb\u7f51\u7edc\uff08\u540c\u4e00\u5957\u9876\u70b9\uff0c\u6709\u4e24\u79cd\u4e0d\u540c\u72b6\u6001\u2014\u2014\\(\\pm 1\\)\u2014\u2014\u7684\u53ef\u4ee5\u5728\u5404\u81ea\u7684\u7f51\u7edc\u4e0a\u4f20\u64ad\\(\\Omega^{\\pm 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