Asymptotic behaviors for functionals of random dynamical systems. Issue 2 (3rd March 2016)

• Record Type: Journal Article
• Authors: Gao, Fuqing; Wang, Shaochen
• Is Part Of: Stochastic analysis and applications. Volume 34:Issue 2(2016)
• Page Start: 258
• Page End: 277
• Publication Date: 2016-03-03
• Subjects: Dynamical system -- forward-backward SDE -- Gaussian approximation -- large deviations -- moderate deviations; 60F10 -- 60H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2015.1119050
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: In this article, we consider asymptotic behaviors for functionals of dynamical systems with small random perturbations. First, we present a deviation inequality for Gaussian approximation of dynamical systems with small random perturbations under Hölder norms and establish the moderate deviation principle and the central limit theorem for the dynamical systems by the deviation inequality. Then, applying these results to forward-backward stochastic differential equations and diffusions in small time intervals, combining the delta method in large deviations, we give a moderate deviation principle for solutions of forward-backward stochastic differential equations with small random perturbations, and obtain the central limit theorem, the moderate deviation principle and the iterated logarithm law for functionals of diffusions in small time intervals.