,A FIRST-ORDER NUMERICAL SCHEME FOR FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN BOUNDED DO

来源 :计算数学(英文版) | 被引量 : 0次 | 上传用户:youtodown1
下载到本地 , 更方便阅读
声明 : 本文档内容版权归属内容提供方 , 如果您对本文有版权争议 , 可与客服联系进行内容授权或下架
论文部分内容阅读
We propose a novel numerical scheme for decoupled forward-backward stochastic differential equations (FBSDEs) in bounded domains,which corresponds to a class of nonlinear parabolic partial differential equations with Dirichlet boundary conditions.The key idea is to exploit the regularity of the solution (Yt,Zt) with respect to Xt to avoid direct approximation of the involved random exit time.Especially,in the one-dimensional case,we prove that the probability of Xt exiting the domain within △t is on the order of O((△t)ε exp(-1/(△t)2ε)),if the distance between the start point X0 and the boundary is at least on the order of O((△t)1/2-ε) for any fixed ε > 0.Hence,in spatial discretization,we set the mesh size △x ~ O((△t)1/2-ε),so that all the interior grid points are sufficiently far from the boundary,which makes the error caused by the exit time decay sub-exponentially with respect to △t.The accuracy of the approximate solution near the boundary can be guaranteed by means of high-order piecewise polynomial interpolation.Our method is developed using the implicit Euler scheme and cubic polynomial interpolation,which leads to an overall first-order convergence rate with respect to △t.
其他文献
1991年,江苏省建湖县杂交水稻种子生产经历了百年罕见的特大洪涝灾害后,获得了令人欣喜的好收成。全县27620亩汕优63等制种组合,总产503.35万公斤,平均亩产182公斤,是自1977
In this paper,a novel multisymplectic scheme is proposed for the coupled nonlinearSchr(o)dinger-KdV (CNLS-KdV) equations.The CNLS-KdV equations are rewritten in
In this paper,we present two alteating direction methods for the solution and best approximate solution of the Sylvester-type matrix equation AXB + CXTD =E aris
皮皮龙和杨丹丹爱上了绿豆——一些小小的,泛着绿莹莹的光的豆子。他们两个谁也不爱吃绿豆,哪怕是把绿豆炖成汤或是煮得开花变成绿豆稀饭。这是绿豆最最普通的用途,一点魅力
In this paper,a split-step θ (SST) method is introduced and used to solve the non-linear neutral stochastic differential delay equations with Poisson jumps (NS
进入大众化时期的中国高等教育,其质量受到社会的广泛关注,建立具有中国特色的高等教育质量保障体系,是确保高等教育持续、健康发展的前提.本文通过国外几种典型的高等教育质
甜瓜(Cucumis melo L.)是世界十大水果之一。网纹甜瓜(Cucumis melo L.var.reticulatus Nand)因果皮美观独特,风味芳香浓郁而深受广大消费者欢迎。但网纹甜瓜多为呼吸跃变型