Asymptotic behavior of densities for stochastic functional differential equations
Asymptotic behavior of densities for stochastic functional differential equations
复制标题
随机泛函微分方程密度的渐近行为
DOI：
10.1155/2013/537023
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
A. Kitagawa and A. Takeuchi
中科院分区：
文献类型：
--
作者：
J. Jaros;T. Kusano and T. Tanigawa;Y. Komori;M. Kato;A. Kitagawa and A. Takeuchi
考虑依赖于有限时间区间内的整个过去历史的随机泛函微分方程，它决定了非马尔可夫过程。在扩散项系数的一致椭圆条件下，解关于勒贝格测度存在光滑密度。本文主要研究解过程族的大偏差和密度的渐近行为。Malliavin演算在我们的论证中起着至关重要的作用。
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.