"Feynman-Kac formula"의 두 판 사이의 차이
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==introduction== | ==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 | + | * The classical Feynman-Kac formula states the connection between |
| − | * 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 | + | ** 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 | ||
2014년 9월 6일 (토) 22:09 판
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
articles
- Pham, Huyen. “Feynman-Kac Representation of Fully Nonlinear PDEs and Applications.” arXiv:1409.0625 [math], September 2, 2014. http://arxiv.org/abs/1409.0625.