"\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u2014 \u041A\u0430\u0446\u0430"@uk . . . . . . . . "In matematica, la formula di Feynman-Kac, il cui nome si deve ai suoi autori Richard Feynman e Mark Kac, \u00E8 un'equazione che fornisce una rappresentazione della soluzione di alcune classi di equazioni alle derivate parziali (PDE) utilizzando le propriet\u00E0 probabilistiche dei processi stocastici."@it . . "Het Feynman-Kac-formalisme is een wiskundige formule die een bijzonder verband legt tussen een parti\u00EBle differentiaalvergelijking en een stochastisch proces. Het is genoemd naar de theoretisch natuurkundige Richard Feynman en de wiskundige Mark Kac."@nl . . . . "F\u00F3rmula de Feynman\u2013Kac"@pt . . "\u30D5\u30A1\u30A4\u30F3\u30DE\u30F3\u2013\u30AB\u30C3\u30C4\u306E\u516C\u5F0F\uFF08\u30D5\u30A1\u30A4\u30F3\u30DE\u30F3\u2013\u30AB\u30C3\u30C4\u306E\u3053\u3046\u3057\u304D\u3001Feynman\u2013Kac formula\uFF09\u3068\u306F\u3001\u653E\u7269\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306E\u30B3\u30FC\u30B7\u30FC\u554F\u984C\u306E\u89E3\u3092\u3001\u30A6\u30A3\u30FC\u30CA\u30FC\u904E\u7A0B\u3092\u7528\u3044\u3066\u8868\u73FE\u3057\u305F\u516C\u5F0F\u306E\u3053\u3068\u3067\u3042\u308B\u3002"@ja . . "Der Satz von Feynman-Kac ist ein Ergebnis der Wahrscheinlichkeitstheorie, das z. B. in der Finanzmathematik Anwendung findet. Er verbindet die Wahrscheinlichkeitstheorie mit der Theorie der partiellen Differentialgleichungen. Der Name geht auf Richard Feynman und Mark Kac zur\u00FCck."@de . . "\u30D5\u30A1\u30A4\u30F3\u30DE\u30F3\u2013\u30AB\u30C3\u30C4\u306E\u516C\u5F0F"@ja . . "\uD30C\uC778\uBA3C-\uCE74\uCE20 \uACF5\uC2DD"@ko . . . . . "Feynman-Kac-formalisme"@nl . . "1114613218"^^ . "630017"^^ . . . . "\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430-\u041A\u0430\u0446\u0430, \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0420\u0456\u0447\u0430\u0440\u0434\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u0456 \u041C\u0430\u0440\u043A\u0430 \u041A\u0430\u0446\u0430 \u2014 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0432\u0437\u0430\u0454\u043C\u043E\u0437\u0432'\u044F\u0437\u043A\u0443 \u043C\u0456\u0436 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F\u043C\u0438 \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u0456 \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0438\u043C\u0438 \u043F\u0440\u043E\u0446\u0435\u0441\u0430\u043C\u0438. \u0417 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u0446\u0456\u0454\u0457 \u0444\u043E\u0440\u043C\u0443\u043B\u0438 \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0432'\u044F\u0437\u0443\u0432\u0430\u0442\u0438 \u043F\u0435\u0432\u043D\u0456 \u0442\u0438\u043F\u0438 \u0420\u0427\u041F \u0437\u0430 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u0441\u0438\u043C\u0443\u043B\u044F\u0446\u0456\u0457 \u0442\u0440\u0430\u0454\u043A\u0442\u043E\u0440\u0456\u0439 \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0456\u0432. \u041D\u0430\u0432\u043F\u0430\u043A\u0438, \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0456 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0432'\u044F\u0437\u0443\u0432\u0430\u0442\u0438 \u043C\u0435\u0442\u043E\u0434\u0430\u043C\u0438 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u0438\u0445 \u0420\u0427\u041F \u0431\u0435\u0437 \u0437\u0430\u043B\u0443\u0447\u0435\u043D\u043D\u044F \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0438\u0445 \u043C\u0435\u0442\u043E\u0434\u0456\u0432."@uk . . . . . . . . . . "\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u2014 \u041A\u0430\u0446\u0430 \u2014 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0444\u043E\u0440\u043C\u0443\u043B\u0430, \u0443\u0441\u0442\u0430\u043D\u0430\u0432\u043B\u0438\u0432\u0430\u044E\u0449\u0430\u044F \u0441\u0432\u044F\u0437\u044C \u043C\u0435\u0436\u0434\u0443 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C\u0438 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F\u043C\u0438 \u0441 \u0447\u0430\u0441\u0442\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u043C\u0438 (\u0441\u043F\u0435\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0442\u0438\u043F\u0430) \u0438 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430\u043C\u0438. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0444\u0438\u0437\u0438\u043A\u0430 \u0420\u0438\u0447\u0430\u0440\u0434\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041C\u0430\u0440\u043A\u0430 \u041A\u0430\u0446\u0430. \u0412 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u044D\u0442\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0434\u0430\u0435\u0442 \u043C\u0435\u0442\u043E\u0434 \u0440\u0435\u0448\u0435\u043D\u0438\u044F \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0441 \u0447\u0430\u0441\u0442\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u043C\u0438 \u0441 \u043F\u043E\u043C\u043E\u0449\u044C\u044E \u0442\u0440\u0430\u0435\u043A\u0442\u043E\u0440\u0438\u0439 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430 (\u0442\u0430\u043A \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u043C\u044B\u0439 \u043C\u0435\u0442\u043E\u0434 \u041C\u043E\u043D\u0442\u0435-\u041A\u0430\u0440\u043B\u043E). \u0418 \u043D\u0430\u043E\u0431\u043E\u0440\u043E\u0442, \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043E\u0436\u0438\u0434\u0430\u043D\u0438\u0435 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u043E \u043A\u0430\u043A \u0440\u0435\u0448\u0435\u043D\u0438\u0435 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0449\u0435\u0433\u043E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0441 \u0447\u0430\u0441\u0442\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u043C\u0438."@ru . . . "\u8D39\u66FC\uFF0D\u5361\u8328\u516C\u5F0F\u662F\u4E00\u4E2A\u6570\u5B66\u516C\u5F0F\u4E0E\u5B9A\u7406\uFF0C\u5F97\u540D\u4E8E\u7406\u67E5\u5FB7\u00B7\u8D39\u66FC\u548C\uFF0C\u5C06\u968F\u673A\u8FC7\u7A0B\u548C\u629B\u7269\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u7ED3\u5408\u5728\u4E00\u8D77\u3002\u4F7F\u7528\u8D39\u66FC\uFF0D\u5361\u8328\u516C\u5F0F\u53EF\u4EE5\u901A\u8FC7\u5C06\u67D0\u4E9B\u629B\u7269\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u89E3\u5199\u6210\u968F\u673A\u8FC7\u7A0B\u7684\u6761\u4EF6\u671F\u671B\u7684\u65B9\u5F0F\uFF0C\u4ECE\u800C\u5C06\u6C42\u6B64\u7C7B\u5FAE\u5206\u65B9\u7A0B\u7684\u6570\u503C\u89E3\u8F6C\u5316\u4E3A\u6A21\u62DF\u968F\u673A\u8FC7\u7A0B\u7684\u8DEF\u5F84\u3002\u53CD\u8FC7\u6765\uFF0C\u6B64\u4E00\u7C7B\u968F\u673A\u8FC7\u7A0B\u7684\u671F\u671B\u53EF\u4EE5\u901A\u8FC7\u786E\u5B9A\u6027\u7684\u8BA1\u7B97\uFF08\u504F\u5FAE\u5206\u65B9\u7A0B\u6C42\u89E3\uFF09\u5F97\u5230\u3002\u8003\u8651\u504F\u5FAE\u5206\u65B9\u7A0B\uFF1A \u6EE1\u8DB3\u8FB9\u754C\u6761\u4EF6\uFF1A \u5176\u4E2D\u7684 \u662F\u5DF2\u77E5\u7684\u51FD\u6570\uFF0C \u662F\u7ED9\u5B9A\u7684\u53C2\u6570\uFF0C \u662F\u6240\u6C42\u7684\u89E3\u51FD\u6570\u3002\u8D39\u66FC\uFF0D\u5361\u8328\u516C\u5F0F\u58F0\u660E\uFF0C\u8FD9\u4E2A\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u89E3\u51FD\u6570\u53EF\u4EE5\u5199\u6210\u67D0\u4E2A\u968F\u673A\u8FC7\u7A0B\u7684\uFF08\u6761\u4EF6\uFF09\u671F\u671B\uFF1A \u5176\u4E2D \u662F\u7531\u4EE5\u4E0B\u7684\u968F\u673A\u52A8\u529B\u65B9\u7A0B \u51B3\u5B9A\u7684\u4F0A\u85E4\u968F\u673A\u8FC7\u7A0B\u3002\u5176\u4E2D\u7684\u662F\u7EF4\u7EB3\u8FC7\u7A0B\uFF08Wiener\u8FC7\u7A0B\uFF0C\u53C8\u79F0\u4E3A\u5E03\u6717\u8FC7\u7A0B\uFF09\uFF0C \u6EE1\u8DB3\u521D\u59CB\u6761\u4EF6\u3002"@zh . . . . . . . . "The Feynman\u2013Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations (PDEs) and stochastic processes. In 1947, when Kac and Feynman were both Cornell faculty, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. The Feynman\u2013Kac formula resulted, which proves rigorously the real case of Feynman's path integrals. The complex case, which occurs when a particle's spin is included, is still unproven. It offers a method of solving certain partial differential equations by simulating random paths of a stochastic process. Conversely, an important class of expectations of random processes can be computed by deterministic methods."@en . . . "Het Feynman-Kac-formalisme is een wiskundige formule die een bijzonder verband legt tussen een parti\u00EBle differentiaalvergelijking en een stochastisch proces. Het is genoemd naar de theoretisch natuurkundige Richard Feynman en de wiskundige Mark Kac."@nl . "In matematica, la formula di Feynman-Kac, il cui nome si deve ai suoi autori Richard Feynman e Mark Kac, \u00E8 un'equazione che fornisce una rappresentazione della soluzione di alcune classi di equazioni alle derivate parziali (PDE) utilizzando le propriet\u00E0 probabilistiche dei processi stocastici."@it . . "Formula di Feynman-Kac"@it . . "A f\u00F3rmula de Feynman\u2013Kac, que recebe este nome em homenagem ao f\u00EDsico norte-americano Richard Feynman e ao matem\u00E1tico polon\u00EAs Mark Kac, estabelece uma liga\u00E7\u00E3o entre equa\u00E7\u00F5es diferenciais parciais (EDPs) parab\u00F3licas e processos estoc\u00E1sticos. A f\u00F3rmula oferece um m\u00E9todo para resolver algumas EDPs pela simula\u00E7\u00E3o de caminhos aleat\u00F3rios de um processo estoc\u00E1stico. Reciprocamente, uma importante classe de valores esperados de processos aleat\u00F3rios pode ser computada por m\u00E9todos determin\u00EDsticos."@pt . . . . . . . "\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u2014 \u041A\u0430\u0446\u0430 \u2014 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u0430\u044F \u0444\u043E\u0440\u043C\u0443\u043B\u0430, \u0443\u0441\u0442\u0430\u043D\u0430\u0432\u043B\u0438\u0432\u0430\u044E\u0449\u0430\u044F \u0441\u0432\u044F\u0437\u044C \u043C\u0435\u0436\u0434\u0443 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043D\u0446\u0438\u0430\u043B\u044C\u043D\u044B\u043C\u0438 \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F\u043C\u0438 \u0441 \u0447\u0430\u0441\u0442\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u043C\u0438 (\u0441\u043F\u0435\u0446\u0438\u0430\u043B\u044C\u043D\u043E\u0433\u043E \u0442\u0438\u043F\u0430) \u0438 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430\u043C\u0438. \u041D\u0430\u0437\u0432\u0430\u043D\u0430 \u0432 \u0447\u0435\u0441\u0442\u044C \u0444\u0438\u0437\u0438\u043A\u0430 \u0420\u0438\u0447\u0430\u0440\u0434\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u0438 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0430 \u041C\u0430\u0440\u043A\u0430 \u041A\u0430\u0446\u0430. \u0412 \u0447\u0430\u0441\u0442\u043D\u043E\u0441\u0442\u0438, \u044D\u0442\u0430 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0434\u0430\u0435\u0442 \u043C\u0435\u0442\u043E\u0434 \u0440\u0435\u0448\u0435\u043D\u0438\u044F \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0441 \u0447\u0430\u0441\u0442\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u043C\u0438 \u0441 \u043F\u043E\u043C\u043E\u0449\u044C\u044E \u0442\u0440\u0430\u0435\u043A\u0442\u043E\u0440\u0438\u0439 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430 (\u0442\u0430\u043A \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u043C\u044B\u0439 \u043C\u0435\u0442\u043E\u0434 \u041C\u043E\u043D\u0442\u0435-\u041A\u0430\u0440\u043B\u043E). \u0418 \u043D\u0430\u043E\u0431\u043E\u0440\u043E\u0442, \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u0447\u0435\u0441\u043A\u043E\u0435 \u043E\u0436\u0438\u0434\u0430\u043D\u0438\u0435 \u0441\u043B\u0443\u0447\u0430\u0439\u043D\u043E\u0433\u043E \u043F\u0440\u043E\u0446\u0435\u0441\u0441\u0430 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u0432\u044B\u0447\u0438\u0441\u043B\u0435\u043D\u043E \u043A\u0430\u043A \u0440\u0435\u0448\u0435\u043D\u0438\u0435 \u0441\u043E\u043E\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0443\u044E\u0449\u0435\u0433\u043E \u0443\u0440\u0430\u0432\u043D\u0435\u043D\u0438\u044F \u0441 \u0447\u0430\u0441\u0442\u043D\u044B\u043C\u0438 \u043F\u0440\u043E\u0438\u0437\u0432\u043E\u0434\u043D\u044B\u043C\u0438."@ru . "\u30D5\u30A1\u30A4\u30F3\u30DE\u30F3\u2013\u30AB\u30C3\u30C4\u306E\u516C\u5F0F\uFF08\u30D5\u30A1\u30A4\u30F3\u30DE\u30F3\u2013\u30AB\u30C3\u30C4\u306E\u3053\u3046\u3057\u304D\u3001Feynman\u2013Kac formula\uFF09\u3068\u306F\u3001\u653E\u7269\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u5F0F\u306E\u30B3\u30FC\u30B7\u30FC\u554F\u984C\u306E\u89E3\u3092\u3001\u30A6\u30A3\u30FC\u30CA\u30FC\u904E\u7A0B\u3092\u7528\u3044\u3066\u8868\u73FE\u3057\u305F\u516C\u5F0F\u306E\u3053\u3068\u3067\u3042\u308B\u3002"@ja . "A f\u00F3rmula de Feynman\u2013Kac, que recebe este nome em homenagem ao f\u00EDsico norte-americano Richard Feynman e ao matem\u00E1tico polon\u00EAs Mark Kac, estabelece uma liga\u00E7\u00E3o entre equa\u00E7\u00F5es diferenciais parciais (EDPs) parab\u00F3licas e processos estoc\u00E1sticos. A f\u00F3rmula oferece um m\u00E9todo para resolver algumas EDPs pela simula\u00E7\u00E3o de caminhos aleat\u00F3rios de um processo estoc\u00E1stico. Reciprocamente, uma importante classe de valores esperados de processos aleat\u00F3rios pode ser computada por m\u00E9todos determin\u00EDsticos."@pt . . . "The Feynman\u2013Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations (PDEs) and stochastic processes. In 1947, when Kac and Feynman were both Cornell faculty, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. The Feynman\u2013Kac formula resulted, which proves rigorously the real case of Feynman's path integrals. The complex case, which occurs when a particle's spin is included, is still unproven."@en . "Der Satz von Feynman-Kac ist ein Ergebnis der Wahrscheinlichkeitstheorie, das z. B. in der Finanzmathematik Anwendung findet. Er verbindet die Wahrscheinlichkeitstheorie mit der Theorie der partiellen Differentialgleichungen. Der Name geht auf Richard Feynman und Mark Kac zur\u00FCck."@de . . . . . . . . . "Feynman-Kac-Formel"@de . . . . . "\u8D39\u66FC\uFF0D\u5361\u8328\u516C\u5F0F"@zh . . "Feynman\u2013Kac formula"@en . . "\u8D39\u66FC\uFF0D\u5361\u8328\u516C\u5F0F\u662F\u4E00\u4E2A\u6570\u5B66\u516C\u5F0F\u4E0E\u5B9A\u7406\uFF0C\u5F97\u540D\u4E8E\u7406\u67E5\u5FB7\u00B7\u8D39\u66FC\u548C\uFF0C\u5C06\u968F\u673A\u8FC7\u7A0B\u548C\u629B\u7269\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u7ED3\u5408\u5728\u4E00\u8D77\u3002\u4F7F\u7528\u8D39\u66FC\uFF0D\u5361\u8328\u516C\u5F0F\u53EF\u4EE5\u901A\u8FC7\u5C06\u67D0\u4E9B\u629B\u7269\u578B\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u89E3\u5199\u6210\u968F\u673A\u8FC7\u7A0B\u7684\u6761\u4EF6\u671F\u671B\u7684\u65B9\u5F0F\uFF0C\u4ECE\u800C\u5C06\u6C42\u6B64\u7C7B\u5FAE\u5206\u65B9\u7A0B\u7684\u6570\u503C\u89E3\u8F6C\u5316\u4E3A\u6A21\u62DF\u968F\u673A\u8FC7\u7A0B\u7684\u8DEF\u5F84\u3002\u53CD\u8FC7\u6765\uFF0C\u6B64\u4E00\u7C7B\u968F\u673A\u8FC7\u7A0B\u7684\u671F\u671B\u53EF\u4EE5\u901A\u8FC7\u786E\u5B9A\u6027\u7684\u8BA1\u7B97\uFF08\u504F\u5FAE\u5206\u65B9\u7A0B\u6C42\u89E3\uFF09\u5F97\u5230\u3002\u8003\u8651\u504F\u5FAE\u5206\u65B9\u7A0B\uFF1A \u6EE1\u8DB3\u8FB9\u754C\u6761\u4EF6\uFF1A \u5176\u4E2D\u7684 \u662F\u5DF2\u77E5\u7684\u51FD\u6570\uFF0C \u662F\u7ED9\u5B9A\u7684\u53C2\u6570\uFF0C \u662F\u6240\u6C42\u7684\u89E3\u51FD\u6570\u3002\u8D39\u66FC\uFF0D\u5361\u8328\u516C\u5F0F\u58F0\u660E\uFF0C\u8FD9\u4E2A\u504F\u5FAE\u5206\u65B9\u7A0B\u7684\u89E3\u51FD\u6570\u53EF\u4EE5\u5199\u6210\u67D0\u4E2A\u968F\u673A\u8FC7\u7A0B\u7684\uFF08\u6761\u4EF6\uFF09\u671F\u671B\uFF1A \u5176\u4E2D \u662F\u7531\u4EE5\u4E0B\u7684\u968F\u673A\u52A8\u529B\u65B9\u7A0B \u51B3\u5B9A\u7684\u4F0A\u85E4\u968F\u673A\u8FC7\u7A0B\u3002\u5176\u4E2D\u7684\u662F\u7EF4\u7EB3\u8FC7\u7A0B\uFF08Wiener\u8FC7\u7A0B\uFF0C\u53C8\u79F0\u4E3A\u5E03\u6717\u8FC7\u7A0B\uFF09\uFF0C \u6EE1\u8DB3\u521D\u59CB\u6761\u4EF6\u3002"@zh . . "10905"^^ . . . . . . . "\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430-\u041A\u0430\u0446\u0430, \u043D\u0430\u0437\u0432\u0430\u043D\u0430 \u043D\u0430 \u0447\u0435\u0441\u0442\u044C \u0420\u0456\u0447\u0430\u0440\u0434\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u0456 \u041C\u0430\u0440\u043A\u0430 \u041A\u0430\u0446\u0430 \u2014 \u0444\u043E\u0440\u043C\u0443\u043B\u0430 \u0432\u0437\u0430\u0454\u043C\u043E\u0437\u0432'\u044F\u0437\u043A\u0443 \u043C\u0456\u0436 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F\u043C\u0438 \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u0456 \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0438\u043C\u0438 \u043F\u0440\u043E\u0446\u0435\u0441\u0430\u043C\u0438. \u0417 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u0446\u0456\u0454\u0457 \u0444\u043E\u0440\u043C\u0443\u043B\u0438 \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0432'\u044F\u0437\u0443\u0432\u0430\u0442\u0438 \u043F\u0435\u0432\u043D\u0456 \u0442\u0438\u043F\u0438 \u0420\u0427\u041F \u0437\u0430 \u0434\u043E\u043F\u043E\u043C\u043E\u0433\u043E\u044E \u0441\u0438\u043C\u0443\u043B\u044F\u0446\u0456\u0457 \u0442\u0440\u0430\u0454\u043A\u0442\u043E\u0440\u0456\u0439 \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0438\u0445 \u043F\u0440\u043E\u0446\u0435\u0441\u0456\u0432. \u041D\u0430\u0432\u043F\u0430\u043A\u0438, \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0456 \u0440\u0456\u0432\u043D\u044F\u043D\u043D\u044F \u0447\u0430\u0441\u0442\u0438\u043D\u043D\u0438\u0445 \u043F\u043E\u0445\u0456\u0434\u043D\u0438\u0445 \u043C\u043E\u0436\u043D\u0430 \u0440\u043E\u0437\u0432'\u044F\u0437\u0443\u0432\u0430\u0442\u0438 \u043C\u0435\u0442\u043E\u0434\u0430\u043C\u0438 \u0437\u0432\u0438\u0447\u0430\u0439\u043D\u0438\u0445 \u0420\u0427\u041F \u0431\u0435\u0437 \u0437\u0430\u043B\u0443\u0447\u0435\u043D\u043D\u044F \u0441\u0442\u043E\u0445\u0430\u0441\u0442\u0438\u0447\u043D\u0438\u0445 \u043C\u0435\u0442\u043E\u0434\u0456\u0432."@uk . "\uD655\uB960\uB860\uC5D0\uC11C \uD30C\uC778\uBA3C-\uCE74\uCE20 \uACF5\uC2DD(Feynman-Kac\u516C\u5F0F, \uC601\uC5B4: Feynman\u2013Kac formula)\uC740 \uD655\uB960 \uBBF8\uBD84 \uBC29\uC815\uC2DD\uACFC \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC774 \uC5B4\uB5A4 \uAD00\uACC4\uB97C \uB9FA\uACE0 \uC788\uB294\uC9C0\uB97C \uB098\uD0C0\uB0B8 \uACF5\uC2DD\uC774\uB2E4. \uC774 \uACF5\uC2DD\uC744 \uD1B5\uD574 \uD2B9\uC815 \uD655\uB960 \uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uD655\uB960 \uACFC\uC815\uC744 \uCC3E\uAE30 \uC704\uD574\uC11C \uC5B4\uB5A4 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uD480\uC5B4\uC57C \uD558\uB294\uC9C0\uB97C \uC54C \uC218 \uC788\uC73C\uBA70, \uB530\uB77C\uC11C \uC774 \uACF5\uC2DD\uC740 \uAE08\uC735\uACF5\uD559\uC5D0\uC11C \uC5B4\uB5A4 \uC790\uC0B0\uC774 \uC774\uD1A0 \uD655\uB960 \uACFC\uC815\uC744 \uB530\uB974\uB294 \uAC83\uC73C\uB85C \uAC00\uC815\uD588\uC744 \uB54C \uC774 \uC790\uC0B0\uC744 \uAE30\uCD08\uC790\uC0B0\uC73C\uB85C \uD558\uB294 \uD30C\uC0DD\uC0C1\uD488\uC758 \uAC00\uACA9\uC744 \uC5B4\uB5BB\uAC8C \uAD6C\uD574\uC57C \uD558\uB294\uC9C0\uC5D0 \uB300\uD55C \uD574\uB2F5\uC744 \uCC3E\uAE30 \uC704\uD55C \uB3C4\uAD6C\uB85C \uC720\uC6A9\uD558\uAC8C \uC4F0\uC774\uACE0 \uC788\uB2E4. \uD30C\uC778\uBA3C-\uCE74\uCE20 \uACF5\uC2DD\uC758 \uAE30\uBCF8\uC801\uC778 \uADFC\uAC70\uB294 \uC5B4\uB5A4 \uD568\uC218 \uAC00 \uB9C8\uD305\uAC8C\uC77C\uC77C \uACBD\uC6B0 \uBBF8\uBD84 \uACC4\uC218 \uC5D0\uC11C \uC2DC\uAC04 \uC5D0 \uB300\uD55C \uBCC0\uD654\uC728\uC744 \uB098\uD0C0\uB0B4\uB294 \uD56D\uC778 \uAC00 \uBC18\uB4DC\uC2DC 0\uC774\uB77C\uB294 \uB370 \uC788\uB2E4. \uB530\uB77C\uC11C \uB9CC\uC57D \uB97C 0\uC73C\uB85C \uB9CC\uB4E4 \uC218 \uC788\uB294 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uCC3E\uC744 \uC218 \uC788\uB2E4\uBA74 \uC774\uB97C \uD480\uC774\uD568\uC73C\uB85C\uC368 \uB97C \uBC1C\uACAC\uD560 \uC218 \uC788\uB2E4\uB294 \uAC83\uC774 \uD30C\uC778\uBA3C-\uCE74\uCE20 \uACF5\uC2DD\uC758 \uD575\uC2EC\uC801\uC778 \uB0B4\uC6A9\uC774\uB2E4. \uC774 \uACF5\uC2DD\uC740 \uCD08\uAE30 \uC870\uAC74 \uAC00 \uC8FC\uC5B4\uC9C4 \uC774\uD1A0 \uD655\uB960 \uACFC\uC815 \uC5D0 \uB300\uD55C \uBCF4\uB810 \uAC00\uCE21 \uD568\uC218 \uAC00 \uC2DC\uC810 \uC5D0 \uAC16\uB294 \uAC12\uC5D0 \uB300\uD55C \uC2DC\uC810 \uC758 \uAE30\uB313\uAC12 \uAC00 \uB9C8\uD305\uAC8C\uC77C\uC784\uC744 \uC774\uC6A9\uD558\uC5EC \uB97C \uCC3E\uC544\uB0B4\uAE30 \uC704\uD574\uC11C \uD480\uC5B4\uC57C \uD560 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uACFC \uD480\uC774\uC5D0 \uD544\uC694\uD55C \uCD5C\uC885 \uC870\uAC74\uC744 \uBC1D\uD600\uB0B8\uB2E4."@ko . . "\u0424\u043E\u0440\u043C\u0443\u043B\u0430 \u0424\u0435\u0439\u043D\u043C\u0430\u043D\u0430 \u2014 \u041A\u0430\u0446\u0430"@ru . . "\uD655\uB960\uB860\uC5D0\uC11C \uD30C\uC778\uBA3C-\uCE74\uCE20 \uACF5\uC2DD(Feynman-Kac\u516C\u5F0F, \uC601\uC5B4: Feynman\u2013Kac formula)\uC740 \uD655\uB960 \uBBF8\uBD84 \uBC29\uC815\uC2DD\uACFC \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC774 \uC5B4\uB5A4 \uAD00\uACC4\uB97C \uB9FA\uACE0 \uC788\uB294\uC9C0\uB97C \uB098\uD0C0\uB0B8 \uACF5\uC2DD\uC774\uB2E4. \uC774 \uACF5\uC2DD\uC744 \uD1B5\uD574 \uD2B9\uC815 \uD655\uB960 \uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uB9CC\uC871\uC2DC\uD0A4\uB294 \uD655\uB960 \uACFC\uC815\uC744 \uCC3E\uAE30 \uC704\uD574\uC11C \uC5B4\uB5A4 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uD480\uC5B4\uC57C \uD558\uB294\uC9C0\uB97C \uC54C \uC218 \uC788\uC73C\uBA70, \uB530\uB77C\uC11C \uC774 \uACF5\uC2DD\uC740 \uAE08\uC735\uACF5\uD559\uC5D0\uC11C \uC5B4\uB5A4 \uC790\uC0B0\uC774 \uC774\uD1A0 \uD655\uB960 \uACFC\uC815\uC744 \uB530\uB974\uB294 \uAC83\uC73C\uB85C \uAC00\uC815\uD588\uC744 \uB54C \uC774 \uC790\uC0B0\uC744 \uAE30\uCD08\uC790\uC0B0\uC73C\uB85C \uD558\uB294 \uD30C\uC0DD\uC0C1\uD488\uC758 \uAC00\uACA9\uC744 \uC5B4\uB5BB\uAC8C \uAD6C\uD574\uC57C \uD558\uB294\uC9C0\uC5D0 \uB300\uD55C \uD574\uB2F5\uC744 \uCC3E\uAE30 \uC704\uD55C \uB3C4\uAD6C\uB85C \uC720\uC6A9\uD558\uAC8C \uC4F0\uC774\uACE0 \uC788\uB2E4. \uD30C\uC778\uBA3C-\uCE74\uCE20 \uACF5\uC2DD\uC758 \uAE30\uBCF8\uC801\uC778 \uADFC\uAC70\uB294 \uC5B4\uB5A4 \uD568\uC218 \uAC00 \uB9C8\uD305\uAC8C\uC77C\uC77C \uACBD\uC6B0 \uBBF8\uBD84 \uACC4\uC218 \uC5D0\uC11C \uC2DC\uAC04 \uC5D0 \uB300\uD55C \uBCC0\uD654\uC728\uC744 \uB098\uD0C0\uB0B4\uB294 \uD56D\uC778 \uAC00 \uBC18\uB4DC\uC2DC 0\uC774\uB77C\uB294 \uB370 \uC788\uB2E4. \uB530\uB77C\uC11C \uB9CC\uC57D \uB97C 0\uC73C\uB85C \uB9CC\uB4E4 \uC218 \uC788\uB294 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uC744 \uCC3E\uC744 \uC218 \uC788\uB2E4\uBA74 \uC774\uB97C \uD480\uC774\uD568\uC73C\uB85C\uC368 \uB97C \uBC1C\uACAC\uD560 \uC218 \uC788\uB2E4\uB294 \uAC83\uC774 \uD30C\uC778\uBA3C-\uCE74\uCE20 \uACF5\uC2DD\uC758 \uD575\uC2EC\uC801\uC778 \uB0B4\uC6A9\uC774\uB2E4. \uC774 \uACF5\uC2DD\uC740 \uCD08\uAE30 \uC870\uAC74 \uAC00 \uC8FC\uC5B4\uC9C4 \uC774\uD1A0 \uD655\uB960 \uACFC\uC815 \uC5D0 \uB300\uD55C \uBCF4\uB810 \uAC00\uCE21 \uD568\uC218 \uAC00 \uC2DC\uC810 \uC5D0 \uAC16\uB294 \uAC12\uC5D0 \uB300\uD55C \uC2DC\uC810 \uC758 \uAE30\uB313\uAC12 \uAC00 \uB9C8\uD305\uAC8C\uC77C\uC784\uC744 \uC774\uC6A9\uD558\uC5EC \uB97C \uCC3E\uC544\uB0B4\uAE30 \uC704\uD574\uC11C \uD480\uC5B4\uC57C \uD560 \uD3B8\uBBF8\uBD84 \uBC29\uC815\uC2DD\uACFC \uD480\uC774\uC5D0 \uD544\uC694\uD55C \uCD5C\uC885 \uC870\uAC74\uC744 \uBC1D\uD600\uB0B8\uB2E4."@ko . . . .