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Sinc-Multistep Schemes for forward backward stochastic differential equations

Advances in Applied Mathematics and Mechanics 2023年第3期15卷 737-768页

作者： Xu Wang Weidong Zhao School of Mathematics&Institute of Finance Shandong UniversityJinanShandong 250100China

In this work,by combining the multistep discretization in time and the Sinc quadrature rule for approximating the conditional mathematical expectations,we will propose new fully discrete multistep schemes called“Sinc-multistep schemes”for forward backward stochastic differential equations(FBSDEs).The schemes avoid spatial interpolations and admit high order of *** stability and the K-th order error estimates in time for the K-step Sinc multistep schemes are theoretically proved(1≤K≤6).This seems to be the first time for analyzing fully time-space discrete multistep schemes for *** examples are also presented to demonstrate the effectiveness,stability,and high order of convergence of the proposed schemes.

关键词： forward backward stochastic differential equations multistep schemes Sinc quadrature rule error estimates

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Second-order schemes for solving decoupled forward backward stochastic differential equations

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Science China Mathematics 2014年第4期57卷 665-686页

作者： ZHAO WeiDong LI Yang FU Yu School of Mathematics Shandong University College of Science University of Shanghai for Science and Technology

In this paper,by using trapezoidal rule and the integration-by-parts formula of Malliavin calculus,we propose three new numerical schemes for solving decoupled forward-backward stochastic differential *** theoretically prove that the schemes have second-order convergence *** demonstrate the effectiveness and the second-order convergence rate,numerical tests are given.

关键词： forward backward stochastic differential equations second-order scheme error estimate trape-zoidal rule Malliavin calculus

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A MAXIMUM PRINCIPLE APPROACH TO stochastic H_2/H_∞ CONTROL WITH RANDOM JUMPS

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Acta Mathematica Scientia 2015年第2期35卷 348-358页

作者：张启侠孙启良 School of Mathematical Sciences University of Jinan

A necessary maximum principle is given for nonzero-sum stochastic Oltterential games with random jumps. The result is applied to solve the H2/H∞ control problem of stochastic systems with random jumps. A necessary and sufficient condition for the existence of a unique solution to the H2/H∞ control problem is derived. The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.

关键词： Nonzero-sum stochastic differential games maximum principle Poisson process stochastic H2/H∞ control forward backward stochastic differential equations

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Convergence Analysis of Kernel Learning FBSDE Filter

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Communications in Mathematical Research 2024年第3期40卷 313-342页

作者： Yunzheng Lyu Feng Bao Department of Mathematics Florida State UniversityFL 32306USA

Kernel learning forward backward stochastic differential equations(FBSDE)filter is an iterative and adaptive meshfree approach to solve the non-linear filtering *** builds from forward backward SDE for Fokker-Planker equation,which defines evolving density for the state variable,and employs kernel density estimation(KDE)to approximate *** algo-rithm has shown more superior performance than mainstream particle filter method,in both convergence speed and efficiency of solving high dimension ***,this method has only been shown to converge *** this paper,we present a rigorous analysis to demonstrate its local and global convergence,and provide theoretical support for its empirical results.

关键词： forward backward stochastic differential equations kernel density estima-tion nonlinear filtering problems convergence analysis.

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