Asymptotic properties of coupled forward-backward stochastic differential equations

Author(s)

Cruzeiro, Ana Bela ^{[1, 2]} ; Gomes, Andre de Oliveira ^{[3, 4]} ; Zhang, Liangquan ^{[5, 6]}

Affiliation

^[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

• Document type: Journal article
• Source: Stochastics and Dynamics; v. 14, n. 3 SEP 2014.
• Web of Science Citations: 1

Abstract

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. (AU)

• FAPESP's process: 11/50151-0 - Dynamical phenomena in complex networks: fundamentals and applications
• Grantee: Elbert Einstein Nehrer Macau
• Support type: Research Projects - Thematic Grants