Asymptotic properties of coupled forward-backward stochastic differential equations

被引：3

作者：

Cruzeiro, Ana Bela ^{[1
,2
]}

Gomes, Andre de Oliveira ^{[3
,4
]}

Zhang, Liangquan ^{[5
,6
]}

机构：

[1] GFMUL, P-1049001 Lisbon, Portugal

[2] Dept Matemat IST TUL, P-1049001 Lisbon, Portugal

[3] Univ Lisbon, GFMUL Grp Fis Matemat, P-1649003 Lisbon, Portugal

[4] Humboldt Univ, Inst Math, Berlin, Germany

[5] Shandong Univ, Sch Math, Jinan, Shandong, Peoples R China

[6] Univ Bretagne Occidentale, Math Lab, F-29285 Brest, France

来源：

STOCHASTICS AND DYNAMICS | 2014年 / 14卷 / 03期

基金：

巴西圣保罗研究基金会;

关键词：

Forward-backward stochastic differential equations; large deviation principle; Meyer-Zheng topology; LARGE DEVIATION PRINCIPLE;

D O I：

10.1142/S021949371450004X

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we consider coupled forward-backward stochastic differential equations (FBSDEs in short) with parameter epsilon > 0, of the following type {X-epsilon,X-t,X-x(s) = x + integral(s)(t) f(r,X-epsilon,X-t,X-x(r),Y epsilon(,t,x)(r))dr +root epsilon integral(s)(t) sigma(r, X-epsilon,X-t,X-x (r), Y-epsilon,Y-t,Y-x(r)) dW(r), Y-epsilon,Y-t,Y-x(s) = h(X-epsilon,X-t,X-x(T)) + integral(T)(s) g(r, X-epsilon,X-t,X-x(r), Y-epsilon,Y-t,Y-x(r), Z(epsilon,t,x)(r)) dr -integral(T)(s) Z(epsilon,t,x)(r) dW(r), 0 <= t <= s <= T. We study the asymptotic behavior of its solutions and establish a large deviation principle for the corresponding processes.

引用

页数：42

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