Publications

All of my recent papers and preprints are on arXiv Preprint Server. They may be slightly different from the published versions.

A Book in Japanese

• "Rahupasu riron to kakuritsu kaiseki" from "Iwanami Shoten, Publishers" (August 2022).
  岩波数学叢書　「ラフパス理論と確率解析」　2022年8月。

Refereed Papers

• Moderate deviations for for two-time scale systems with mixed fractional Brownian motion.
  (with Yong Xu and Xiaoyu Yang).
  Appl. Math. Optim. 90 (2024), no. 1, Paper No. 18, 41 pages.
  
  
• Moderate deviations for rough differential equations.
  (with Yong Xu and Xiaoyu Yang).
  Bull. Lond. Math. Soc. 56 (2024), no. 8, 2538--2548.
  
  
• Wong-Zakai approximation of density functions.
  Preprint, 35 pages. arXiv: 2304.01449.
  
  
• Large deviation principle for slow-fast system with mixed fractional Brownian motion.
  (with Yong Xu and Xiaoyu Yang).
  Preprint, 25 pages. arXiv: 2303.06626.
  
  
• Support theorem for pinned diffusion processes.
  Nagoya Math. J., 253 (2024), 241--264.
  
  
• Averaging principle for slow-fast systems of rough differential equations via controlled paths.
  To appear in Tohoku Math. J., 44 pages. arXiv: 2210.01334.
  
  
• Large deviations for small noise hypoelliptic diffusion bridges on sub-Riemannian manifolds.
  Publ. Res. Inst. Math. Sci. 60 (2024), no.1, 145--184.
  
  
• Averaging principle for fast-slow system driven by mixed fractional Brownian rough path.
  (with Bin Pei and Yong Xu).
  J. Differential Equations 301 (2021), 202--235.
  (Corrigendum. J. Differential Equations 355 (2023), 437--440.)
  
  
• Positivity of the density for rough differential equations.
  (with Bin Pei).
  J. Theoret. Probab. 35 (2022), no. 3, 1863--1877.
  
  
• Pathwise unique solutions and stochastic averaging for mixed stochastic partial differential equations driven by fractional Brownian motion and Brownian motion.
  (with Bin Pei and Yong Xu).
  To appear in Stoch. Anal. Appl., 35 pages. arXiv:2004.05305.
  
  
• Averaging principles for mixed fast-slow systems driven by fractional Brownian motion.
  (with Bin Pei and Yong Xu).
  Kyoto J. Math. 63 (2023), no. 4, 721--748.
  
  
• Stochastic flows and rough differential equations on foliated spaces.
  (with Kiyotaka Suzaki).
  Bull. Sci. Math. 160 (2020) 102852, 29 pages.
  
  
• Asymptotic expansion of the density for hypoelliptic rough differential equation.
  (with Nobuaki Naganuma).
  Nagoya Math. J., 243 (2021), 11--41.
  
  
• Paracontrolled quasi-geostrophic equation with space-time white noise.
  (with Yoshihiro Sawano).
  Dissertationes Math. 558 (2020), 1--81. 60 (35).
  
  
• Heat trace asymptotics on equiregular sub-Riemannian manifolds.
  (with Setsuo Taniguchi).
  J. Math. Soc. Japan 72, No. 4 (2020), 1049--1096.
  
  
• Stochastic complex Ginzburg-Landau equation with space-time white noise.
  (with Masato Hoshino and Nobuaki Naganuma).
  Electron. J. Probab. 22, (2017), paper no. 104, 68 pages.
  
  
• Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus.
  (with Setsuo Taniguchi).
  Forum Math. Sigma 5 (2017), e16, 74 pp.
  
  
• Rough path theory and stochastic analysis.
  Sugaku Expositions 32, no. 1 (2019), 113--136.
  (This is an English translation of my survey article in Japanese. You can find a PDF file at the bottom of this webpage or at arXiv:1602.03255.)
  
  
• Large deviations for rough path lifts of Watanabe's pullbacks of delta functions.
  Int. Math. Res. Not., IMRN 2016, no. 20, 6378-6414.
  
  
• Short time kernel asymptotics for rough differential equation driven by fractional Brownian motion.
  Electron. J. Probab. 21 (2016), paper no. 34, 1-29.
  
  
• Malliavin differentiability of solutions of rough differential equations.
  J. Funct. Anal. 267 (2014), 1566-1584.
  
  
• Large deviation principle for certain spatially lifted Gaussian rough path.
  Tohoku Math. J. 67 (2015) no. 3, 433-463.
  
  
• Large deviation principle of Freidlin-Wentzell type for pinned diffusion processes.
  Trans. Amer. Math. Soc. 367 (2015), 8107-8137.
  
  
• Short time kernel asymptotics for Young SDE by means of Watanabe distribution theory.
  J. Math. Soc. Japan 68, No. 2 (2016), 1--43.
  
  
• A moment estimate for the derivative process in rough path theory.
  Proc. Amer. Math. Soc. 140 (2012), 2183-2191.
  
  
• Laplace approximation for rough differential equation driven by fractional Brownian motion.
  Ann. Probab. 41 (2013), No. 1, 170-205.
  
  
• A note on rough differential equations with unbounded coefficients.
  Probabilistic approach to geometry, 155--170, Adv. Stud. Pure Math., 57, Math. Soc. Japan, Tokyo, 2010.
  
  
• A stochastic Taylor-like expansion in the rough path theory.
  J. Theoret. Probab. 23 (2010), Issue 3, 671--714.
  
  
• On the Laplace-type asymptotics and the stochastic Taylor expansion for Itô functionals of Brownian rough paths.
  (with Hiroshi Kawabi).
  RIMS Kokyuroku Bessatsu B6 (2008), 139--152.
  
  
• Asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths.
  (with Hiroshi Kawabi).
  J. Funct. Anal. 243 (2007), no. 1, 270--322.
  
  
• On asymptotics of Banach space-valued Itô functionals of Brownian rough paths.
  (with Hiroshi Kawabi).
  Stochastic Analysis and Applications--The Abel symposium 2005, Stockholm, Springer, 415-434, (2007).
  
  
• Quasi-sure existence of Brownian rough paths and a construction of Brownian pants.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top. 9 (2006), No. 4, 513--528.
  
  
• Laplace's method for the laws of heat processes on loop spaces.
  J. Funct. Anal. 232 (2006), no. 1, 148--194.
  
  
• Large deviations for heat kernel measures on loop spaces via rough paths.
  (with Hiroshi Kawabi).
  J. London Math. Soc. (2) 73 (2006), no. 3, 797--816.
  
  
• On the heat trace of the magnetic Schrödinger operators on the hyperbolic plane.
  (with Shin-ichi Shirai).
  Math. Phys. Electron. J. 12 (2006), no. 12, 46 pages.
  
  
• On the piecewise geodesic approximation of Andersson and Driver.
  Osaka J. Math. 42 (2005), no. 4, 791--806.
  
  
• Eigenvalue asymptotics for the Schrödinger operators on the real and the complex hyperbolic spaces.
  (with Shin-ichi Shirai).
  J. Math. Pures Appl. (9), 83 (2004), no. 5, 589--627.
  
  
• Eigenvalue asymptotics for the Schrödinger operators on the hyperbolic plane.
  (with Shin-ichi Shirai).
  J. Funct. Anal. 211 (2004), no. 2, 424--456.
  
  
• Spectral properties of Pauli operators on the Poincaré upper-half plane.
  (with Shin-ichi Shirai).
  J. Math. Phys. 44 (2003), no. 6, 2451--2462.
  
  
• Logarithmic Sobolev inequality for $H_0^s$-metric on pinned loop groups.
  Infin. Dimens. Anal. Quantum Probab. Relat. Top. 7 (2004), No. 1, 1--26.
  
  
• The essential spectrum of Schrödinger operators with asymptotically constant magnetic fields on the Poincaré upper-half plane.
  (with Shin-ichi Shirai).
  J. Math. Phys. 44 (2003), no. 1, 89--106.
  
  
• Convergence of finite dimensional distributions of heat kernel measures on loop groups.
  J. Funct Anal. 198 (2003), no. 2, 311 - 340.
  
  
• Explicit lower bound of the Ricci tensor on free loop algebras.
  J. Math. Kyoto Univ. 42 (2002), No. 3, 465--475.
  
  
• Logarithmic Sobolev inequality on free loop groups for heat kernel measures associated with the general Sobolev spaces.
  J. Funct. Anal. 179 (2001), no. 1, 170--213.
  
  
• Some estimates of the logarithmic Sobolev constants on manifolds with boundary and an application to the Ising models.
  J. Math. Kyoto Univ. 41 (2001), No. 2, 359--386.
  
  
• Meyer's inequality of the type $L(¥log L)^{¥alpha}$ on abstract Wiener space.
  J. Math. Kyoto Univ. 39 (1999), No. 1, 87--113.
  
  

A survey article in Japanese

• "Rahupasu riron to kakuritsu kaiseki" in "Sugaku" (July 2015).
  An English translation titled as "Rough path theory and stochastic analysis" is "here"

An Edited Book

• "Stochastic Analysis, Random Fields and Integrable Probability — Fukuoka 2019"
  Editors: Yuzuru Inahama, Hirofumi Osada, Tomoyuki Shirai. Adv. Stud. Pure Math., 87: 429pp. (2021).