On the absolute continuity of one-dimensional SDEs driven by a fractional Brownian motion. (English) Zbl 1091.60008

Summary: The problem of absolute continuity for a class of SDEs driven by a real fractional Brownian motion of any Hurst index is addressed. First, we give an elementary proof of the fact that when the diffusion coefficient does not vanish, the solution to the SDE has a positive density for all \(t>0\). Second, we extend in our setting the classical entrance-time criterion of N. Bouleau and F. Hirsch [J. Funct. Anal. 69, 229–259 (1986; Zbl 0605.60058)].


60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G18 Self-similar stochastic processes


Zbl 0605.60058
Full Text: DOI


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