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.
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Acknowledgements
The first named author was partially supported by JSPS KAKENHI (JP20H01807) and Grant-in-Aid for JSPS Fellows (JP18F18314). The second named author was partially supported by the National Natural Science Foundation of China (11802216, 12172285), the Fundamental Research Funds for the Central Universities, the Young Talent fund of University Association for Science and Technology in Shaanxi, China, and JSPS Grant-in-Aid for JSPS Fellows (JP18F18314).
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Inahama, Y., Pei, B. Positivity of the Density for Rough Differential Equations. J Theor Probab 35, 1863–1877 (2022). https://doi.org/10.1007/s10959-021-01116-2
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DOI: https://doi.org/10.1007/s10959-021-01116-2