Local Hölder Continuity Property of the Densities of Solutions of SDEs with Singular Coefficients

Masafumi Hayashi (), Arturo Kohatsu-Higa () and Gô Yûki ()
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Masafumi Hayashi: University of the Ryukyus, and Japan Science and Technology Agency
Arturo Kohatsu-Higa: Ritsumeikan University and Japan Science and Technology Agency
Gô Yûki: Ritsumeikan University and Japan Science and Technology Agency

Journal of Theoretical Probability, 2013, vol. 26, issue 4, 1117-1134

Abstract: Abstract We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and Hölder continuous drift has a Hölder continuous density function. This result complements recent results of Fournier–Printems (Bernoulli 16(2):343–360, 2010), where the density is shown to exist if both coefficients are Hölder continuous, and exemplifies the role of the drift coefficient in the regularity of the density of a diffusion.

Keywords: Malliavin Calculus; Non-smooth drift; Density function; 60H07; 60H10 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-012-0430-7

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