"Feynman-Kac formula"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
||
| (다른 사용자 한 명의 중간 판 4개는 보이지 않습니다) | |||
| 1번째 줄: | 1번째 줄: | ||
==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 | ||
| + | * [[Fokker–Planck equation]] | ||
| + | |||
| + | |||
| + | ==related items== | ||
| + | * [[Feynman diagrams and path integral]] | ||
| + | |||
==articles== | ==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. | * Pham, Huyen. “Feynman-Kac Representation of Fully Nonlinear PDEs and Applications.” arXiv:1409.0625 [math], September 2, 2014. http://arxiv.org/abs/1409.0625. | ||
| − | |||
| − | |||
| − | |||
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.