Survey on Path-Dependent PDEs  

作　　者：Shige PENG Yongsheng SONG Falei WANG 

机构地区：[1]School of Mathematics,Zhongtai Securities Institute for Financial Studies,Shandong University,Jinan 250100,China [2]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [4]Zhongtai Securities Institute for Financial Studies,School of Mathematics,Shandong University,Jinan 250100,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第6期837-856,共20页数学年刊（B辑英文版）

基　　金：supported by the National Key R&D Program of China(Nos.2018YFA0703900,2020YFA0712700,2018YFA0703901);the National Natural Science Foundation of China(Nos.12031009,12171280);the Natural Science Foundation of Shandong Province(Nos.ZR2021YQ01,ZR2022JQ01).

摘　　要：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 Fréchet)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.

关 键 词：Path-Dependent Wiener expectation BSDES Classical solution Sobolev solution Viscosity solution 

分 类 号：O175.2[理学—数学]