GAUSSIAN-TYPE LOWER BOUNDS FOR THE DENSITY OF SOLUTIONS OF SDES DRIVEN BY FRACTIONAL BROWNIAN MOTIONS

• 成果类型: Article
• 署名作者: Besalu, M.; Kohatsu-Higa, A.; Tindel, S.
• 署名单位: Universite de Lorraine; Universite de Lorraine; Ritsumeikan University; Japan Science & Technology Agency (JST)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP977
• 发表日期: 2016
• 页码: 399-443
• 关键词: differential-equations driven; stochastic calculus; malliavin calculus; Respect

摘要

In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter H. In the one-dimensional case with additive noise, our study encompasses all parameters H is an element of (0, 1), while the multidimensional case is restricted to the case H > 1/2. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.