Asymptotic Behavior of Densities for Stochastic Functional Differential Equations. (28th February 2013)

• Record Type: Journal Article
• Authors: Kitagawa, Akihiro; Takeuchi, Atsushi
• Other Names: Mohammed S. Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2013(2013)
• Publication Date: 2013-02-28
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2013/537023
• Languages: English
• ISSNs: 2090-3332

Abstract

Abstract : Consider stochastic functional differential equations depending on whole past histories in a finite time interval, which determine non-Markovian processes. Under the uniformly elliptic condition on the coefficients of the diffusion terms, the solution admits a smooth density with respect to the Lebesgue measure. In the present paper, we will study the large deviations for the family of the solution process and the asymptotic behaviors of the density. The Malliavin calculus plays a crucial role in our argument.