{"id":44448,"date":"2023-08-09T19:59:06","date_gmt":"2023-08-09T11:59:06","guid":{"rendered":"https:\/\/swarma.org\/?p=44448"},"modified":"2023-08-09T19:59:06","modified_gmt":"2023-08-09T11:59:06","slug":"%e4%bf%9d%e7%bd%97%c2%b7%e5%88%97%e7%bb%b4%e7%9a%84%e9%bb%91%e5%a4%a9%e9%b9%85%ef%bc%9a%e7%a6%bb%e7%be%a4%e5%80%bc%e7%9a%84%e7%89%a9%e7%90%86%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=44448","title":{"rendered":"\u4fdd\u7f57\u00b7\u5217\u7ef4\u7684\u201c\u9ed1\u5929\u9e45\u201d\uff1a\u79bb\u7fa4\u503c\u7684\u7269\u7406\u5b66"},"content":{"rendered":"
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David D. Nolte<\/span><\/span> | \u4f5c\u8005<\/span><\/strong><\/section>\n
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\u4f8b\u5982\uff0c1870\u5e74\u751f\u7269\u5b66\u5bb6\u6258\u9a6c\u65af\u00b7\u8d6b\u80e5\u9ece<\/span>\uff08Thomas Henry Huxley\uff09<\/span>\u56e0\u70ed\u8877\u4e8e\u634d\u536b\u8fbe\u5c14\u6587\u7684\u7406\u8bba\u800c\u88ab\u79f0\u4e3a\u201c\u8fbe\u5c14\u6587\u7684\u6597\u725b\u72ac\u201d\uff0c\u4ed6\u5728\u82f1\u56fd\u5229\u7269\u6d66\u53d1\u8868\u4e86\u4e00\u6b21\u6f14\u8bb2\uff0cNature<\/em> \u6742\u5fd7\u63f4\u5f15\u4ed6\u7684\u8bdd\uff1a\u201c\u2026\u2026\u79d1\u5b66\u7684\u4f1f\u5927\u60b2\u5267\u2014\u2014\u4e00\u4e2a\u4e11\u964b\u7684\u4e8b\u5b9e\u627c\u6740\u4e86\u4e00\u4e2a\u7f8e\u4e3d\u7684\u5047\u8bf4\u3002\u201d<\/span><\/section>\n

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1973\u5e74\uff0c\u8d39\u820d\u5c14\u00b7\u5e03\u83b1\u514b<\/span>\uff08Fischer Black\uff09<\/span>\u548c\u8fc8\u4f26\u00b7\u65af\u79d1\u5c14\u65af<\/span>\uff08Myron Scholes\uff09<\/span>\u63d0\u51fa\u4e00\u4e2a\u7f8e\u4e3d\u7684\u7ecf\u6d4e\u7406\u8bba\uff0c\u4f5c\u4e3a\u5728\u534e\u5c14\u8857\u8fdb\u884c\u5b8c\u7f8e\u5957\u671f\u4fdd\u503c\u7684\u4e00\u79cd\u65b9\u6cd5\uff0c\u636e\u79f0\u8be5\u7406\u8bba\u6ca1\u6709\u98ce\u9669\uff0c\u4f46\u5374\u80fd\u4fdd\u8bc1\u80a1\u4ef7\u5927\u8d77\u5927\u843d\u65f6\u4ecd\u83b7\u5f97\u6b63\u6536\u76ca\u30021994\u5e74\uff0c\u65af\u79d1\u5c14\u65af\u548c\u5e03\u83b1\u514b\u6210\u7acb\u4e86\u4e00\u5bb6\u6295\u8d44\u516c\u53f8\uff0c\u5c06\u8fd9\u4e00\u7f8e\u4e3d\u7684\u7406\u8bba\u53d8\u4e3a\u73b0\u5b9e\uff0c\u6295\u8d44\u56de\u62a5\u7387\u8fbe\u5230\u4ee4\u4eba\u96be\u4ee5\u7f6e\u4fe1\u7684 40%\u3002\u5e03\u83b1\u514b\u4e8e1995\u5e74\u53bb\u4e16\uff0c\u65af\u79d1\u5c14\u65af\u5374\u57281997\u5e74\u83b7\u5f97\u8bfa\u8d1d\u5c14\u7ecf\u6d4e\u5b66\u5956\u3002\u7b2c\u4e8c\u5e74\uff0c\u8be5\u57fa\u91d1\u5012\u95ed\uff0c\u4ee4\u5e03\u83b1\u514b-\u65af\u79d1\u5c14\u65af\u8499\u7f9e\u7684\u4e11\u964b\u4e8b\u5b9e\u662f\u9ed1\u5929\u9e45\u3002<\/span><\/section>\n

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\u4f46\u9ed1\u5929\u9e45\u51fa\u73b0\u4e86\uff0c\u5b83\u7684\u6570\u503c\u51fa\u4e4e\u610f\u6599\uff0c\u4e0e\u5176\u4ed6\u6240\u6709\u6d4b\u91cf\u7ed3\u679c\u90fd\u4e0d\u4e00\u6837\uff0c\u4ee5\u81f3\u4e8e\u4eba\u4eec\u5e38\u5e38\u8ba4\u4e3a\u5b83\u662f\u9519\u8bef\u7684\uff0c\u751a\u81f3\u53ef\u80fd\u5c06\u5176\u4e22\u5f03\uff0c\u56e0\u4e3a\u5b83\u7834\u574f\u4e86\u539f\u672c\u4e0d\u9519\u7684\u7edf\u8ba1\u6570\u636e\uff0c\u8fd9\u4e00\u6570\u636e\u70b9\u4ee5\u4e0d\u53ef\u5ffd\u7565\u7684\u65b9\u5f0f\u626d\u66f2\u4e86\u5e73\u5747\u503c\u548c\u6807\u51c6\u5dee\u3002\u5bf9\u4e8e\u8fd9\u79cd\u4ee4\u4eba\u5fc3\u70e6\u7684\u4e8b\u4ef6\uff0c\u4eba\u4eec\u7684\u53cd\u5e94\u662f\u83b7\u53d6\u66f4\u591a\u6570\u636e\uff0c\u8ba9\u5e73\u5747\u503c\u518d\u6b21\u7a33\u5b9a\u4e0b\u6765\u2026..\u76f4\u5230\u53e6\u4e00\u4e2a\u9ed1\u5929\u9e45\u51fa\u73b0\uff0c\u518d\u6b21\u504f\u79bb\u5e73\u5747\u503c\u3002\u7136\u800c\uff0c\u8fd9\u79cd\u5f02\u5e38\u503c<\/span>\uff08outlier\uff09<\/span>\u5f80\u5f80\u4e0d\u662f\u865a\u5047\u7684\u6d4b\u91cf\u7ed3\u679c\uff0c\u5374\u662f\u6d4b\u91cf\u8fc7\u7a0b\u7684\u81ea\u7136\u7ec4\u6210\u90e8\u5206\uff0c\u5728\u4e0d\u5f71\u54cd\u7814\u7a76\u7edf\u8ba1\u5b8c\u6574\u6027\u7684\u60c5\u51b5\u4e0b\uff0c\u4e0d\u5e94\u8be5\u4e5f\u4e0d\u53ef\u80fd\u5c06\u5176\u5254\u9664\u3002<\/span><\/section>\n

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2007\u5e74\uff0c\u4f5c\u5bb6\u5854\u52d2\u5e03<\/span>\uff08Nassim Nicholas Taleb\uff09<\/span>\u5728\u5176\u6781\u5177\u5f71\u54cd\u529b\u7684\u8457\u4f5c\u300a\u9ed1\u5929\u9e45\uff1a\u6781\u4e0d\u53ef\u80fd\u4e8b\u4ef6\u7684\u5f71\u54cd\u300b<\/span>\uff08The Black Swan: The Impact of the Highly Improbable<\/em>\uff09<\/span>\u4e2d\u6307\u51fa\uff0c\u65e0\u8bba\u662f\u5546\u4e1a\u3001\u65b0\u6280\u672f\u5f00\u53d1\u3001\u9009\u4e3e\u8fd8\u662f\u91d1\u878d\u5e02\u573a\u884c\u4e3a\uff0c\u79bb\u7fa4\u503c\u73b0\u8c61\u51e0\u4e4e\u662f\u73b0\u4ee3\u751f\u6d3b\u65b9\u65b9\u9762\u9762\u7684\u6838\u5fc3\u90e8\u5206\u3002\u770b\u4f3c\u8868\u73b0\u826f\u597d\u7684\u4e8b\u7269\uff0c\u4e00\u5957\u4ea7\u54c1\u3001\u4e00\u4e2a\u96c6\u4f53\u793e\u4f1a\u6216\u4e00\u7cfb\u5217\u653f\u5e9c\u653f\u7b56\uff0c\u7a81\u7136\u88ab\u4e00\u9879\u65b0\u53d1\u660e\u3001\u4e00\u9879\u65b0\u6cd5\u5f8b\u3001\u4e00\u9879\u6700\u9ad8\u6cd5\u9662\u7684\u9519\u8bef\u5224\u51b3\u3001\u4e00\u573a\u6218\u4e89\u6216\u80a1\u5e02\u5d29\u76d8\u7834\u574f\u3002<\/span><\/section>\n

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\u4ed6\u5bf9\u91d1\u878d\u7406\u8bba\u7684\u8457\u540d\u8d21\u732e\u662f1973\u5e74\u4e0e\u62dc\u4f26\u00b7\u65af\u79d1\u5c14\u65af\u5408\u8457\u7684\u8bba\u6587\u300a\u671f\u6743\u548c\u516c\u53f8\u8d1f\u503a\u7684\u5b9a\u4ef7\u300b\u3002\u5957\u671f\u4fdd\u503c\u662f\u534e\u5c14\u8857\u7684\u53e4\u8001\u4f20\u7edf\uff0c\u6307\u7ecf\u7eaa\u4eba\u5356\u51fa\u671f\u6743<\/span>\uff08\u5728\u4ee5\u540e\u4ee5\u7ed9\u5b9a\u7684\u4ef7\u683c\u8d2d\u4e70\u80a1\u7968\uff09<\/span>\uff0c\u5047\u5b9a\u80a1\u7968\u4f1a\u8d2c\u503c<\/span>\uff08\u5356\u7a7a\uff09<\/span>\uff0c\u7136\u540e\u4e70\u5165\u4e00\u5b9a\u6570\u91cf\u76f8\u540c\u8d44\u4ea7\u7684\u80a1\u7968<\/span>\uff08\u4e70\u591a\uff09<\/span>\uff0c\u4f5c\u4e3a\u4ef7\u683c\u4e0a\u6da8\u7684\u4fdd\u9669\u3002\u5982\u679c\u7ecf\u7eaa\u4eba\u5728\u8db3\u591f\u591a\u7684\u591a\u5934\u80a1\u7968\u548c\u8db3\u591f\u591a\u7684\u7a7a\u5934\u671f\u6743\u4e4b\u95f4\u53d6\u5f97\u5e73\u8861\uff0c\u90a3\u4e48\u6295\u8d44\u7ec4\u5408\u7684\u4ef7\u503c\u5c31\u4e0d\u4f1a\u53d7\u5230\u6807\u7684\u8d44\u4ea7\u4ef7\u503c\u6bcf\u65e5\u6ce2\u52a8\u7684\u5f71\u54cd\u3002<\/span><\/section>\n

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\u8fd9\u79cd\u6295\u8d44\u7ec4\u5408\u5c31\u662f\u53eb\u505a\u91d1\u878d\u884d\u751f\u4ea7\u54c1<\/strong><\/span>\uff08derivative\uff09<\/span>\u7684\u4e00\u79cd\u91d1\u878d\u5de5\u5177\u3002\u4e4b\u6240\u4ee5\u53eb\u884d\u751f\u4ea7\u54c1\uff0c\u662f\u56e0\u4e3a\u6295\u8d44\u7ec4\u5408\u7684\u4ef7\u503c\u6765\u6e90\u4e8e\u76f8\u5173\u8d44\u4ea7\u4ef7\u503c\uff0c\u5176\u9762\u4e34\u7684\u6311\u6218\uff0c\u662f\u5728\u5230\u671f\u524d\u968f\u65f6\u627e\u5230\u5176\u201c\u771f\u5b9e\u201d\u4ef7\u503c\u3002\u5982\u679c\u7ecf\u7eaa\u4eba\u77e5\u9053\u884d\u751f\u54c1\u7684\u201c\u771f\u5b9e\u201d\u4ef7\u503c\uff0c\u90a3\u4e48\u4e70\u5356\u884d\u751f\u54c1\u5c31\u4e0d\u4f1a\u6709\u98ce\u9669\u3002<\/span><\/section>\n

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\u5f53\u4fdd\u7f57\u00b7\u5217\u7ef4<\/span>\uff08Paul L\u00e9vy\uff09\uff081886-1971\u5e74\uff09<\/span>\u4e8e1919\u5e74\u5e94\u9080\u5728\u5df4\u9ece\u7efc\u5408\u7406\u5de5\u5b66\u9662\u53d1\u8868\u4e09\u573a\u5173\u4e8e\u968f\u673a\u53d8\u91cf\u7684\u6f14\u8bb2\u65f6\uff0c\u6982\u7387\u8bba\u7684\u6570\u5b66\u7406\u8bba\u8fd8\u53ea\u662f\u4e00\u79cd\u539f\u7406\u548c\u8bc1\u660e\u7684\u677e\u6563\u96c6\u5408\u3002\u4ece\u8fd9\u4e9b\u8bb2\u5ea7\u4e2d\u4ea7\u751f\u7684\uff0c\u662f\u4ed6\u4e00\u751f\u5bf9\u8fd9\u4e00\u9886\u57df\u7684\u7814\u7a76\uff0c\u5982\u4eca\u8fd9\u4e00\u9886\u57df\u5df2\u53d1\u5c55\u6210\u4e3a\u6570\u5b66\u7684\u4e3b\u8981\u5206\u652f\u4e4b\u4e00\uff0c\u5c3d\u7ba1\u4e8c\u6218\u671f\u95f4\u4ed6\u5728\u7ef4\u5e0c\u6cd5\u56fd\u7684\u53cd\u72b9\u4e3b\u4e49\u73af\u5883\u4e2d\u8270\u96be\u524d\u884c\uff0c\u4f46\u5728\u804c\u4e1a\u751f\u6daf\u4e2d\u6210\u5c31\u5353\u8457\uff0c\u7855\u679c\u7d2f\u7d2f\u3002\u4ed6\u7684\u8bba\u6587\u5bfc\u5e08\u662f\u8457\u540d\u7684\u96c5\u514b\u00b7\u54c8\u8fbe\u739b<\/span>\uff08Jacques Hadamard\uff09<\/span>\uff0c\u4ed6\u7684\u5b66\u751f\u4e4b\u4e00\u662f\u8457\u540d\u7684\u8d1d\u52aa\u74e6\u00b7\u66fc\u5fb7\u5e03\u6d1b\u7279<\/span>\uff08Benoit Mandelbrot\uff09<\/span>\u3002<\/span><\/section>\n

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\u5217\u7ef4\u64b0\u5199\u4e86\u591a\u672c\u5177\u6709\u5f71\u54cd\u529b\u7684\u6559\u79d1\u4e66\uff0c\u5960\u5b9a\u4e86\u6982\u7387\u8bba\u7684\u57fa\u7840\uff0c\u4ed6\u7684\u540d\u5b57\u51e0\u4e4e\u6210\u4e3a\u8fd9\u4e00\u9886\u57df\u7684\u4ee3\u540d\u8bcd\uff0c\u5176\u4e2d\u4e00\u672c\u8457\u4f5c\u662f\u5173\u4e8e\u968f\u673a\u53d8\u91cf\u7684\u52a0\u6cd5\u7406\u8bba[2]\uff0c\u4ed6\u5728\u4e66\u4e2d\u6269\u5c55\u4e86\u7a33\u5b9a\u5206\u5e03<\/span>\uff08stable distribution\uff09<\/span>\u7684\u6982\u5ff5\u3002<\/span><\/section>\n

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\u65e9\u5e74\u7684\u4fdd\u7f57\u00b7\u5217\u7ef4\u3002\uff5c\u6765\u6e90\uff1aAnnales des Mines<\/span><\/section>\n

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\u4ece\u03b1=1\uff08\u67ef\u897f\uff09\u5230\u03b1=2\uff08\u9ad8\u65af\uff09\u53c2\u6570\u8303\u56f4\u5185\u7684\u5bf9\u79f0\u5217\u7ef4\u5206\u5e03\u51fd\u6570\u3002\u03b1<2\u65f6\u7684\u5217\u7ef4\u98de\u884c\u5177\u6709\u7ec6\u83cc\u8fd0\u52a8\u4e2d\u7ecf\u5e38\u51fa\u73b0\u7684\u5954\u8dd1\u548c\u7ffb\u6eda\u884c\u4e3a\u3002<\/span><\/p>\n


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\u5217\u7ef4\u6982\u7387\u5206\u5e03\u51fd\u6570\u7684\u60ca\u4eba\u4e4b\u5904\u5728\u4e8e\uff0c\u5b83\u4eec\u5728\u81ea\u7136\u73b0\u8c61\u4e2d\u5341\u5206\u5e38\u89c1\uff0c\u51e0\u4e4e\u6240\u6709\u5177\u6709\u5c3a\u5ea6\u4e0d\u53d8\u6027<\/strong><\/span>\uff08scale invariance\uff09<\/span>\u7684\u8fc7\u7a0b\u4e2d\u90fd\u4f1a\u51fa\u73b0\u4e25\u91cd\u7684\u5217\u7ef4\u5c3e<\/strong>\u3002\u7136\u800c\uff0c\u4f5c\u4e3a\u5b66\u751f\uff0c\u6211\u4eec\u51e0\u4e4e\u5bf9\u5b83\u4eec\u89c6\u800c\u4e0d\u89c1\uff0c\u4f3c\u4e4e\u6cca\u677e\u548c\u9ad8\u65af\u7edf\u8ba1\u5c31\u662f\u6211\u4eec\u9700\u8981\u77e5\u9053\u7684\u4e00\u5207\uff0c\u4f46\u65e0\u77e5\u5e76\u4e0d\u662f\u5e78\u798f\u3002\u6b63\u662f\u9ad8\u65af\u7edf\u8ba1\u5047\u8bbe\u5bfc\u81f4\u4e86 Black-Scholes \u6a21\u578b\u7684\u5931\u8d25\u3002<\/span><\/section>\n

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\u5c3a\u5ea6\u4e0d\u53d8\u8fc7\u7a0b\u901a\u5e38\u662f\u8d28\u91cf\u6216\u80fd\u91cf\u81ea\u7136\u7ea7\u8054\u7684\u7ed3\u679c\uff0c\u56e0\u6b64\u4f5c\u4e3a\u4e2d\u6027\u73b0\u8c61\u51fa\u73b0\u3002\u7136\u800c\uff0c\u5728\u4e00\u4e9b\u6709\u504f\u73b0\u8c61\u4e2d\uff0c\u5217\u7ef4\u8fc7\u7a0b\u4f1a\u5bfc\u81f4\u67d0\u79cd\u5f62\u5f0f\u7684\u4f18\u5316\uff0c\u751f\u7269\u80cc\u666f\u4e0b\u7684\u5217\u7ef4\u968f\u673a\u6e38\u8d70\u5c31\u662f\u8fd9\u79cd\u60c5\u51b5\u3002<\/span><\/section>\n

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\u968f\u673a\u6e38\u8d70\u662f\u7edf\u8ba1\u7269\u7406\u5b66\u7684\u57fa\u77f3\u4e4b\u4e00\uff0c\u4e5f\u662f\u5e03\u6717\u8fd0\u52a8\u7684\u57fa\u7840\u3002\u7231\u56e0\u65af\u5766\u5229\u7528\u5e03\u6717\u8fd0\u52a8\u63a8\u5bfc\u51fa\u8457\u540d\u7684\u6269\u6563\u7edf\u8ba1\u529b\u5b66\u65b9\u7a0b\uff0c\u8bc1\u660e\u5206\u5b50\u7269\u8d28\u7684\u5b58\u5728\uff1b\u8ba9\u00b7\u4f69\u6797<\/span>\uff08Jean Perrin\uff09<\/span>\u56e0\u5176\u5bf9\u7231\u56e0\u65af\u5766\u7406\u8bba\u7684\u5b9e\u9a8c\u8bc1\u660e\u800c\u83b7\u5f97\u8bfa\u8d1d\u5c14\u5956\uff1b\u6717\u4e4b\u4e07<\/span>\uff08Paul Langevin\uff09<\/span>\u5229\u7528\u5e03\u6717\u8fd0\u52a8\u5c06\u968f\u673a\u5fae\u5206\u65b9\u7a0b\u5f15\u5165\u7edf\u8ba1\u7269\u7406\u5b66\uff1b\u800c\u5217\u7ef4\u5219\u5229\u7528\u5e03\u6717\u8fd0\u52a8\u6765\u8bf4\u660e\u6570\u5b66\u6982\u7387\u8bba\u7684\u5e94\u7528\uff0c\u5e76\u5199\u4e0b\u4e86\u4ed6\u6700\u540e\u4e00\u672c\u9887\u5177\u5f71\u54cd\u529b\u7684\u8457\u4f5c\u3002<\/span><\/section>\n

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\u5bf9\u968f\u673a\u6e38\u8d70\u7684\u5927\u591a\u6570\u7814\u7a76\u90fd\u5047\u5b9a\u6b65\u957f\u6216\u901f\u7387\u4e3a\u9ad8\u65af\u6216\u6cca\u677e\u7edf\u8ba1\uff0c\u4f46\u5f53\u6b65\u957f\u53d6\u81ea\u5217\u7ef4\u5206\u5e03\u65f6\uff0c\u5c31\u4f1a\u51fa\u73b0\u4e00\u79cd\u7279\u6b8a\u5f62\u5f0f\u7684\u968f\u673a\u6e38\u8d70\u3002\u8fd9\u5c31\u662f\u5217\u7ef4\u968f\u673a\u6e38\u8d70\uff0c\u8d1d\u52aa\u74e6\u00b7\u66fc\u5fb7\u5e03\u6d1b\u7279<\/span>\uff08Benoit Mandelbrot\uff09\uff08\u5217\u7ef4\u7684\u5b66\u751f\uff09<\/span>\u5c06\u5176\u547d\u540d\u4e3a\u201c\u5217\u7ef4\u98de\u884c<\/strong>\u201d<\/span>\uff08L\u00e9vy Flight\uff09<\/span>\uff0c\u5e76\u5bf9\u5176\u5206\u5f62\u7279\u5f81\u8fdb\u884c\u7814\u7a76\u3002<\/span><\/section>\n

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\u5217\u7ef4\u968f\u673a\u6e38\u8d70\u6700\u521d\u662f\u4f5c\u4e3a\u7406\u60f3\u6570\u5b66\u6a21\u578b\u6765\u7814\u7a76\u7684\uff0c\u4f46\u8fd1\u5e74\u6765\u5bf9\u5176\u6709\u8bb8\u591a\u53d1\u73b0\uff0c\u5728\u52a8\u7269\u89c5\u98df\u884c\u4e3a\u4e2d\u89c2\u5bdf\u5230\u5217\u7ef4\u968f\u673a\u6e38\u8d70<\/strong>\uff0c\u751a\u81f3\u5728\u7ec6\u83cc\u7684\u5954\u8dd1\u548c\u7ffb\u6eda\u884c\u4e3a\u4e2d\u4e5f\u89c2\u5bdf\u5230\u5217\u7ef4\u968f\u673a\u6e38\u8d70\uff0c\u636e\u63a8\u6d4b\uff0c\u8fd9\u79cd\u89c5\u98df\u7b56\u7565\u80fd\u8ba9\u52a8\u7269\u5bf9\u968f\u673a\u5206\u5e03\u7684\u98df\u7269\u6765\u6e90\u8fdb\u884c\u6700\u4f73\u91c7\u6837\u3002\u6709\u8bc1\u636e\u8868\u660e\uff0c\u5206\u5b50\u5728\u7ec6\u80de\u5185\u8fd0\u8f93\u4e2d\u5b58\u5728\u5217\u7ef4\u884c\u8d70\uff0c\u8fd9\u53ef\u80fd\u6e90\u4e8e\u62e5\u6324\u7684\u7ec6\u80de\u5185\u90bb\u57df\u5185\u7684\u968f\u673a\u8fd0\u52a8\u3002\u4eba\u4eec\u8fd8\u89c2\u5bdf\u5230\u4e00\u79cd\u4e2d\u95f4\u72b6\u6001[4]\uff0c\u5373\u7ec6\u80de\u5185\u7684\u7ec6\u80de\u5668\u548c\u56ca\u6ce1\u5728\u6cbf\u7740\u7ec6\u80de\u9aa8\u67b6\u9644\u7740\u3001\u8fc1\u79fb\u548c\u8131\u79bb\u9a71\u52a8\u5b83\u4eec\u7684\u5206\u5b50\u9a6c\u8fbe\u65f6\uff0c\u53ef\u80fd\u5177\u6709\u5217\u7ef4\u884c\u8d70\u7684\u7279\u5f81\u3002<\/span><\/section>\n

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\u539f\u6587\u94fe\u63a5\uff1a<\/span><\/p>\n

https:\/\/galileo-unbound.blog\/2023\/02\/08\/paul-levys-black-swan-the-physics-of-outliers\/<\/span><\/p>\n


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\u53c2\u8003\u4e66\u76ee\u9009\u7f16<\/strong><\/span><\/section>\n
Paul L\u00e9vy, Calcul des probabilit\u00e9s (Gauthier-Villars, Paris, 1925).<\/span><\/section>\n
Paul L\u00e9vy, Th\u00e9orie de l\u2019addition des variables al\u00e9atoires (Gauthier-Villars, Paris, 1937).<\/span><\/section>\n
Paul L\u00e9vy, Processus stochastique et mouvement brownien (Gauthier-Villars, Paris, 1948).<\/span><\/section>\n
R. Metzler, J. Klafter, The random walk\u2019s guide to anomalous diffusion: a fractional dynamics approach. Physics Reports-Review Section Of Physics Letters 339, 1-77 (2000).<\/span><\/section>\n
J. Klafter, I. M. Sokolov, First Steps in Random Walks : From Tools to Applications.  (Oxford University Press, 2011).<\/span><\/section>\n
F. Hoefling, T. Franosch, Anomalous transport in the crowded world of biological cells. Reports on Progress in Physics 76,  (2013).<\/span><\/section>\n
V. Zaburdaev, S. Denisov, J. Klafter, Levy walks. Reviews of Modern Physics 87, 483-530 (2015).<\/span><\/section>\n

<\/section>\n
\u53c2\u8003\u6587\u732e<\/strong><\/span><\/section>\n
[1] Black, Fischer; Scholes, Myron (1973). \u201cThe Pricing of Options and Corporate Liabilities\u201d. Journal of Political Economy. 81 (3): 637\u2013654.<\/span><\/section>\n
[2] P. L\u00e9vy, Th\u00e9orie de l\u2019addition des variables al\u00e9atoire (1937)<\/span><\/section>\n
[3] The central limit theorem holds if the mean value of a number of N samples converges to a stable value as the number of samples increases to infinity.<\/span><\/section>\n
[4] H. Choi, K. Jeong, J. Zuponcic, E. Ximenes, J. Turek, M. Ladisch, D. D. Nolte, Phase-Sensitive Intracellular Doppler Fluctuation Spectroscopy. Physical Review Applied 15, 024043 (2021).<\/span><\/section>\n

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\u672c\u5b63\u8bfb\u4e66\u4f1a\u8be6\u60c5\u4e0e\u62a5\u540d\u65b9\u5f0f\u8bf7\u53c2\u8003\uff1a<\/span><\/section>\n
\u76f4\u9762\u590d\u6742\u7cfb\u7edf\uff0c\u91cd\u8bc6\u7ecf\u6d4e\u89c4\u5f8b\uff1a\u590d\u6742\u7ecf\u6d4e\u5b66\u8bfb\u4e66\u4f1a\u7b2c\u4e8c\u5b63<\/strong><\/a>
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\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n

1. <\/strong>\u73b0\u4ee3\u6982\u7387\u8bba\u4e4b\u7236\uff1a\u67ef\u5c14\u83ab\u54e5\u6d1b\u592b\u7684\u201c\u968f\u673a\u201d\u4eba\u751f<\/a><\/strong><\/span><\/section>\n
2.<\/strong>  Nature Reviews Physics\uff1a\u7269\u7406\u5b66\u4e2d\u7684\u5e42\u5f8b<\/a><\/strong><\/span><\/section>\n
3. <\/strong><\/strong>\u7c97\u770b\u957f\u5c3e\uff0c\u7ec6\u8fa8\u5e42\u5f8b\uff1a\u8de8\u4e16\u7eaa\u7684\u65e0\u6807\u5ea6\u7f51\u7edc\u7814\u7a76\u7eb7\u4e89\u53f2<\/a><\/strong><\/strong><\/span><\/section>\n
4. <\/strong><\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
<\/a><\/strong><\/strong><\/span><\/section>\n
5. <\/strong><\/strong>\u52a0\u5165\u96c6\u667a\u5b66\u56edVIP\uff0c\u83b7\u5f9720\u5468\u5e74\u201c\u6d8c\u73b0\u201d\u5b66\u672f\u5e74\u4f1a\u5165\u573a\u5238\uff01<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u52a0\u5165\u590d\u6742\u7ecf\u6d4e\u5b66\u8bfb\u4e66\u4f1a<\/strong><\/span><\/strong><\/span><\/strong><\/section>\n

<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u8bf4\u8d77\u6982\u7387\u5206\u5e03\uff0c\u9ad8\u65af\u5206\u5e03\u548c\u6cca\u677e\u5206\u5e03\u4f3c\u4e4e\u662f\u6211\u4eec\u77e5\u9053\u7684\u4e00\u5207\uff0c\u7136\u800c\uff0c\u5217\u7ef4\u5206\u5e03\u5b9e\u9645\u4e0a\u5728\u81ea\u7136\u73b0\u8c61\u4e2d\u5341\u5206\u5e38\u89c1\u3002\u4e00\u79cd\u88ab\u79f0\u4e3a\u201c\u5217\u7ef4\u98de\u884c\u201d\uff08L\u00e9vy flight\uff09\u7684\u968f\u673a\u6e38\u8d70\uff0c\u53ef\u4ee5\u5f88\u597d\u5730\u6a21\u62df\u52a8\u7269\u89c5\u98df\u3001\u80a1\u7968\u4ef7\u683c\u6ce2\u52a8\u3001\u5730\u9707\u548c\u6e4d\u6d41\u7b49\u73b0\u8c61\u3002 \u7814\u7a76\u9886\u57df\uff1a\u9ed1\u5929\u9e45\u4e8b\u4ef6\uff0c\u6982\u7387\u8bba\uff0c\u968f\u673a\u6e38\u8d70\uff0c\u5217\u7ef4\u98de\u884c David D. Nolte&…<\/p>\n","protected":false},"author":0,"featured_media":44429,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/44448"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=44448"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/44448\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/44429"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=44448"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=44448"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=44448"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=44448"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}