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2020년 11월 16일 (월) 09:46 기준 최신판
introduction
- The classical Feynman-Kac formula states the connection between
- linear parabolic partial differential equations (PDEs), like the heat equation, and
- expectation of stochastic processes driven by Brownian motion
- It gives then a method for solving linear PDEs by Monte Carlo simulations of random processes
memo
- One possible source is the book of Brian Hall on quantum mechanics for mathematicians.
- Another possibility is the series on functional analysis by Reed and Simon
- Fokker–Planck equation
articles
- Chen, Le, Yaozhong Hu, and David Nualart. “Two-Point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation.” arXiv:1509.01121 [math], September 3, 2015. http://arxiv.org/abs/1509.01121.
- Pham, Huyen. “Feynman-Kac Representation of Fully Nonlinear PDEs and Applications.” arXiv:1409.0625 [math], September 2, 2014. http://arxiv.org/abs/1409.0625.