TY - JOUR
T1 - Positivity of the Density for Rough Differential Equations
AU - Inahama, Yuzuru
AU - Pei, Bin
N1 - Funding Information:
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).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/9
Y1 - 2022/9
N2 - 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.
AB - 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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U2 - 10.1007/s10959-021-01116-2
DO - 10.1007/s10959-021-01116-2
M3 - Article
AN - SCOPUS:85113644948
SN - 0894-9840
VL - 35
SP - 1863
EP - 1877
JO - Journal of Theoretical Probability
JF - Journal of Theoretical Probability
IS - 3
ER -