Positivity of the Density for Rough Differential Equations

Yuzuru Inahama () and Bin Pei ()
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Yuzuru Inahama: Kyushu University
Bin Pei: Northwestern Polytechnical University

Journal of Theoretical Probability, 2022, vol. 35, issue 3, 1863-1877

Abstract: Abstract Due to recent developments of Malliavin calculus for rough differential equations, it is now known that, under natural assumptions, the law of a unique solution at a fixed time has a smooth density function. Therefore, it is quite natural to ask whether or when the density is strictly positive. In this paper we study this problem from the viewpoint of Aida–Kusuoka–Stroock’s general theory.

Keywords: Gaussian rough path; Malliavin calculus; Positivity of probability density function; 60L20; 60H07; 60G15 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10959-021-01116-2

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