A branching particle system approximation for a class of FBSDEs

作     者：Dejian Chang Huili Liu Jie Xiong 

作者机构：School of MathematicsShandong UniversityJinan 250100People’s Republic of China Department of MathematicsHebei Normal UniversityShijiazhuang 050024People’s Republic of China Department of MathematicsUniversity of MacaoAvenida da UniversidadeTaipaMacaoSpecial Administrative Region of China 

出 版 物：《Probability, Uncertainty and Quantitative Risk》 (概率、不确定性与定量风险（英文）)

年 卷 期：2016年第1卷第1期

页      面：305-338页

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：support by National Science Foundation of China NSFC 11501164 Xiong acknowledges research support by Macao Science and Technology Fund FDCT 076/2012/A3 and MultiYear Research Grants of the University of Macao No.MYRG2014-00015-FST and MYRG2014-00034-FST 

主　　题：Forward-backward stochastic differential equation Partial differential equations Branching particle system Numerical solution 

摘      要：In this paper,a new numerical scheme for a class of coupled forwardbackward stochastic differential equations(FBSDEs)is proposed by using branching particle systems in a random ***,by the four step scheme,we introduce a partial differential Eq.(PDE)used to represent the solution of the FBSDE ***,infinite and finite particle systems are constructed to obtain the approximate solution of the *** location and weight of each particle are governed by stochastic differential equations derived from the FBSDE ***,a branching particle system is established to define the approximate solution of the FBSDE *** branching mechanism of each particle depends on the path of the particle itself during its short lifetim ∈=n^(−2α),where n is the number of initial particles and α1/2 is a fixed *** convergence of the scheme and its rate of convergence are obtained.