Preprint(s)

• Radial processes on RCD^* (K,N) spaces
  (with K. Kuwae)
  (Submitted; pdf file Uploaded at Aug. 22, 2017)
   
• Sub-Laplacian comparison theorems on totally geodesic Riemannian foliations
  (with F. Baudoin, E. Grong and A. Thalmaier)
  (Submitted; arXiv:1706.08489)
   
• Zero noise limit of a stochastic differential equation involving a local time
  (with Taro Matsumura)
  (Submitted; pdf file Uploaded at Oct. 3, 2016)
   
• Equivalence between dimensional contractions in Wasserstein distance and the curvature-dimension condition
  (with François Bolley, Ivan Gentil and Arnaud Guillin)
  (To appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze; pdf file Uploaded at Feb. 27, 2017)
   
• A coupling of Brownian motions in the L_0-geometry
  (with Takafumi Amaba)
  (To appear in Tohoku Mathematical Journal; pdf file Uploaded at Aug. 1, 2014)
   

Refereed papers

• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces
  (with Matthias Erbar and Karl-Theodor Sturm)
  Invent. Math. Vol. 201 no.3 (2015) 993–1071.
   
• Space-time Wasserstein controls and Bakry-Ledoux type gradient estimates
  Calc. Var. Partial Differential Equations Vol. 54 no.1 (2015) 127–161.
   
• Gradient estimate for Markov kernels, Wasserstein control and Hopf-Lax formula
  Potential Theory and its Related Fields, RIMS Kôkyûroku Bessatsu B43 (2013) 61–80.
   
• Monotonicity of time-dependent transportation costs and coupling by reflection
  (with Karl-Theodor Sturm)
  Potential Analysis Vol. 39, no.3 (2013) 231–263.
   
• A probabilistic approach to the maximal diameter theorem
  Mathematische Nachrichten Vol. 286, no.4 (2013) 374–378.
   
• Heat flow on Alexandrov spaces
  (with N. Gigli and S. Ohta)
  Communications on Pure and Applied Mathematics Vol. 66, no.3 (2013) 307–331.
   
• Convergence of time-inhomogeneous geodesic random walks and its application to coupling methods
  (Revision of the paper "Coupling by reflection of diffusion processes via discrete approximation under a backward Ricci flow")
  Annals of Probability Vol. 40, no. 5 (2012) 1945–1979.
   
• Non-explosion of diffusion processes on manifolds with time-dependent metric
  (with R. Philipowski)
  Mathematische Zeitschrift Vol. 268, no. 3 (2011) 979–991.
   
• Coupling of Brownian motions and Perelman's L-functional
  (with R. Philipowski)
  Journal of Functional Analysis Vol. 260, no. 9 (2011) 2742–2766.
   
• Large deviation for stochastic line integrals as L^p-currents
  (with S. Kusuoka and Y. Tamura)
  Probability Theory and Related Fields Vol. 147, no. 3–4 (2010) 649–674.
   
• Duality on gradient estimates and Wasserstein controls
  Journal of Functional Analysis Vol. 258, no. 11 (2010) 3758–3774.
   
• Couplings of the Brownian motion via discrete approximation under lower Ricci curvature bounds
  Probabilistic Approach to Geometry, Adv. Stud. Pure. Math. Vol. 57 (2010) 273–292 .
   
• Characterization of maximal Markovian couplings for diffusion processes
  Electronic Journal of Probability, Vol. 14 (2009) 633–662.
   
• Laplace approximation for stochastic line integrals
  Probability Theory and Related Fields, Vol. 144 (2009) 1–51.
   
• On uniqueness of maximal coupling for diffusion processes with a reflection
  Journal of Theoretical Probability, Vol. 20 (2007) 935–957.
   
• A counterexample for the optimality of Kendall-Cranston coupling
  (with K.-Th. Sturm)
  Electronic Communications in Probability, Vol.12 (2007) 66–72.
   
• On large deviations for random currents induced from stochastic line integrals
  Forum Mathematicum, Vol. 18 (2006) 639–676.
   
• Sample path large deviations for a class of random currents
  Stochastic processes and their applications, Vol. 108 (2003) 203–228.
   

Survey

• The entropic curvature dimension condition and Bochner's inequality
  RIMS Kôkyûroku Vol. 1903 (2014) 102–110 (without being refereed).
   

Book

• 最適輸送理論とリッチ曲率 (in Japanese)
  (桑江一洋氏，塩谷隆氏，太田慎一氏，高津飛鳥氏との共著)
  数学メモアール 第8巻，日本数学会, 2017
   

PhD thesis

On large deviations for current-valued processes induced from stochastic line integrals
pdf file

Last updated Aug. 22, 2017