The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold

Oleg O. Obrezkov

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The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold

机译：紧黎曼流形上热方程的Feynman-Kac公式的证明

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A full proof of the Feynman–Kac-type formula for heat equation on a compact Riemannian manifold is obtained using some ideas originating from the papers of Smolyanov, Truman, Weizsaecker and Wittich.1-3 In particular, the technique exploited in the paper has some common lines with Chernoff theorem, which is one of the basic points of the approach to the topics undertaken in the above-mentioned papers.

机译：利用源自Smolyanov，Truman，Weizsaecker和Wittich论文的一些思想，获得了紧凑的黎曼流形上热方程的Feynman-Kac型公式的完整证明。1-3特别是，本文中使用的技术具有与切尔诺夫定理有一些共同之处，这是上述论文所采用的方法的基本要点之一。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2003年第2期|共10页
作者
Oleg O. Obrezkov;
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正文语种 eng
中图分类物理学;
关键词
Feynman–Kac formula; compact Riemannian manifold; Chernoff theorem; Wiener measure; heat equation;

机译：Feynman–Kac公式;紧黎曼流形;切尔诺夫定理;维纳测度;热方程;

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1. The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold [J] . Oleg O. Obrezkov Infinite dimensional analysis, quantum probability, and related topics . 2003,第2期

机译：紧黎曼流形上热方程的Feynman-Kac公式的证明
2. Feynman and Feynman-Kac formulas for evolution equations with Vladimirov operator [J] . Smolyanov OG, Shamarov NN Doklady. Mathematics . 2008,第3期

机译：使用Vladimirov算子的演化方程的Feynman和Feynman-Kac公式
3. Feynman-Kac and Feynman Formulas for Evolution Pseudodifferential Equations in Superspace [J] . Panyunin NM Russian journal of mathematical physics . 2008,第4期

机译：超空间中演化伪微分方程的Feynman-Kac和Feynman公式
4. Heat Kernel Short-Time Expansion within the Scope of Feynman-Kac Formula [C] . S.A.Stepin, A.J.Rejrat Workshop on Geometrical Methods in Physics . 2010

机译：Feynman-Kac公式范围内的热内核短时间扩张
5. Analysis of conjugate heat equation on complete non-compact Riemannian manifolds under Ricci flow. [D] . Kuang, Shilong. 2009

机译：Ricci流下完全非紧黎曼流形上共轭热方程的分析。
6. SINGULAR INTEGRAL EQUATIONS FOR DIFFERENTIAL FORMS ON RIEMANNIAN MANIFOLDS [O] . J. J. Kohn 1956

机译：Rimannian流形上微分形式的奇异积分方程
7. Two-point correlation function and Feynman-Kac formula for the stochastic heat equation [O] . Chen, Le, Hu, Yaozhong, Nualart, David 2015

机译：两点相关函数与Feynman-Kac公式随机热方程
8. The Heat Equation, the KAC Formula and Some Index Formulas [R] . Duncan, T. E. 1979

机译：热方程，KaC公式和一些指数公式

The Proof of the Feynman–Kac Formula for Heat Equation on a Compact Riemannian Manifold

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