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| Survey on Path-Dependent PDEs* |
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Citation： |
Shige PENG,Yongsheng SONG,Falei WANG.Survey on Path-Dependent PDEs*[J].Chinese Annals of Mathematics B,2023,44(6):837~856 |
| Page view： 1250
Net amount： 730 |
Authors： |
Shige PENG; Yongsheng SONG;Falei WANG |
Foundation： |
National Key R&D Program of China (Nos. 2018YFA0703900, 2020YFA0712700, 2018YFA0703901), the National Natural Science Foundation of China (Nos. 12031009,12171280) and the Natural Science Foundation of Shandong Province (Nos. ZR2021YQ01,ZR2022JQ01) |
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| Abstract： |
In this paper, the authors provide a brief introduction of the path-dependent partial differential equations (PDEs for short) in the space of continuous paths, where the path derivatives are in the Dupire (rather than Fr′echet) sense. They present the connections between Wiener expectation, backward stochastic differential equations (BSDEs for short) and path-dependent PDEs. They also consider the well-posedness of path-dependent PDEs, including classical solutions, Sobolev solutions and viscosity solutions. |
Keywords： |
Path-Dependent, Wiener expectation, BSDEs, Classical solution, Sobolev solution, Viscosity solution |
Classification： |
60H10, 60H30, 35K10 |
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