1. |
Yuzuru Inahama, Support theorem for pinned diffusion processes, *Nagoya Mathematical Journal*, 10.1017/nmj.2023.25, 253, 241-264, 2024.01, In this paper we prove a support theorem of Stroock-Varadhan type for pinned diffusion processes. To this end we use two powerful results from stochastic analysis. One is quasi-sure analysis for Brownian rough path. The other is Aida-Kusuoka-Stroock's positivity theorem for the densities of weighted laws of non-degenerate Wiener functionals.. |

2. |
Yuzuru Inahama, Pei Bin, Positivity of the Density for Rough Differential Equations, *Journal of Theoretical Probability*, https://doi.org/10.1007/s10959-021-01116-2, 35, 1863-1877, 2022.06. |

3. |
Bin Pei, Yuzuru Inahama, Yong Xu, Averaging principle for fast-slow system driven by mixed fractional Brownian rough path, *J. Differential Equations*, https://doi.org/10.1016/j.jde.2021.08.006, 301, 202-235, 2021.11. |

4. |
Yuzuru Inahama, Yoshihiro Sawano., Paracontrolled quasi-geostrophic equation with space-time white noise, *Dissertationes Math.*, 558, 35, 1-81, 2020.08, We study the stochastic dissipative quasi-geostrophic equation with space-time white noise on the two-dimensional torus. This equation is highly singular and basically ill-posed in its original form. The main objective of the present paper is to formulate and solve this equation locally in time in the framework of paracontrolled calculus when the differential order of the main term, the fractional Laplacian, is larger than $7/4$. No renormalization has to be done for this model.. |

5. |
Yuzuru Inahama, Kiyotaka Suzaki, Stochastic flows and rough differential equations on foliated spaces, *Bull. Sci. Math.*, 160, 29 pages, 2020.03. |

6. |
Yuzuru Inahama, Rough path theory and stochastic analysis, *Sugaku Expositions *, 32, 1, 113-136, 2019.01. |

7. |
Masato Hoshino, Yuzuru Inahama, Nubuaki Naganuma,, Stochastic complex Ginzburg-Landau equation with space-time white noise, *Electron. J. Probab.*, no. 22, Paper no. 104, 68 pages, 2017.06. |

8. |
Yuzuru Inahama, Setsuo Taniguchi, Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus, *Forum Math. Sigma*, 5, e16, 74 pages, 2017.06. |

9. |
Yuzuru Inahama, Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion, *Electron. J. Probab. *, no. 21, Paper no. 34, 29 pages, 2016.06. |

10. |
Yuzuru Inahama, Large deviations for rough path lifts of Watanabe's pullbacks of delta functions, *Int. Math. Res. Not.*, IMRN 2016, no. 20, 6378-6414, 2016.06. |

11. |
稲濱 譲, Malliavin differentiability of solutions of rough differential equations, *Journal of Functional Analysis*, 267, 1566-1584, 2016.10, In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a fixed time is smooth in the sense of Malliavin calculus. Examples of Gaussian processes include fractional Brownian motion with Hurst parameter larger than 1/4.. |