Publication List(1990--)

  1. Support Theorem for Diffusion Processes on Hilbert Spaces, Publ.Res.Inst.Math.Sci. 26 (1990), no.6, 947--965.
  2. D^{\infty}-Cohomology Groups and D^{\infty}-Maps on Submanifolds in Wiener Spaces, J. Funct.Anal. 107 (1992), no.2, 289--301.
  3. On the Support of Wiener Functionals (with D.W.Stroock and S.Kusuoka), Asymptotic Problems in Probability Theory: Wiener functonals and asymptotics (Sanda/Kyoto, 1990), 3--34, Pitman Res. Notes Math. Ser., 284, Longman Sci. Tech., Harlow, 1993.
  4. Certain gradient flows and submanifolds in Wiener spaces, J. Funct. Anal. 112 (1993), no.2, 346-372.
  5. On the Ornstein-Uhlenbeck Operators on Wiener-Riemannian Manifolds, J. Funct. Anal. 116(1993), no.1, 83-110.
  6. Sobolev Spaces over Loop Groups, J. Funct. Anal. 127 (1995), no.1, 155-172.
  7. Logarithmic Sobolev Inequalities and Exponential Integrability (with T.Masuda (Kobe University of commerce) and I.Shigekawa (Kyoto University)) J. Funct. Anal. 126 (1994), no.1, 83--101
  8. Logarithmic Sobolev Inequalities and Spectral Gaps : Perturbation Theory, (with I.Shigekawa (Kyoto University)), J. Funct. Anal. 126 (1994),no.2, 448--475.
  9. Moment Estimates Derived From Poincare and Logarithmic Sobolev Inequalities, (with D.Stroock (MIT)) Math. Res. Lett. 1 (1994) no.1, 75-86.
  10. On the Irreducibility of Certain Dirichlet Forms on Loop Spaces over Compact Homogeneous Spaces, New Trends in Stochastic Analysis (Charingworth, 1994), 3--42, World Sci. Publishing, River Edge, NJ, 1997.
  11. Differential calculus on path and loop spaces. I. Logarithmic Sobolev inequalities on path spaces, (with K.D. Elworthy (Warwick University)), C.R.Acad.Sci.Paris Sr. I Math. 321 (1995) no.1, 97--102.
  12. Logarithmic Sobolev Inequalities on Loop Spaces over compact Reimannian Manifolds, Stochastic Analysis and Applications (Powys 1995), 1--19, World Sci. Publishing, River Edge, NJ 1996.
  13. Differential Calculus on Path and Loop Spaces, II Irreducibility of Dirichlet Forms on Loop Spaces, Bull. Sci. Math., 122 (1998), no.8, 635--666.
  14. Gradient Estimates of Harmonic Functions and Asymptotics of Spectral Gaps on Path Sapces, Interdiscip. Inform. Sci. 2 (1996), no.1, 75--84.
  15. Uniform Positivity Improving Property, Sobolev Inequality and Spectral Gaps, J. Funct.Anal., 158 (1998) no.1, 152--185.
  16. Stochastic analysis on loop spaces (Japanese) Sugaku 50 (1998), no.3, 265--281.
  17. Logarithmic derivatives of heat kernels and logarithmic Sobolev inequalities with unbounded diffusion coefficients on loop spaces, J. Funct. Anal. 174 (2000), no.2, 430-477.
  18. Stochastic analysis on loop spaces, (translation of Sugaku 50 (1998) 265--281) Sugaku Expositions 13 (2000), no.2, 197--214.
  19. Equivalence of heat kernel measure and pinned Wiener measure on loop groups, (with Bruce Driver), C. R. Acad. Sci. Paris Sr.I Math. 331 (2000), no.9, 709-712.
  20. On the irreducibility of Dirichlet forms on domains in infinite dimensional spaces, Osaka J. Math. 37, (2000) no.4, 953--966.
  21. Precise Gaussian lower bounds on heat kernels, ``Stochastics in Finite and Infinite Dimensions'', 1--28, Trends Math, Birkh\"auser Boston, Boston MA 2001.
  22. Short time asymptotics of a certain infinite dimensional diffusion process, (with Hiroshi Kawabi), Stochastic Analysis and Related Topics VII, The Silivri Workshop, 77--124, Progress in Probability 48, Birkh\"auser, 2001.
  23. On the small time asymptotics of diffusion processes on path groups, (with T-S.Zhang), Potential Analysis Vol.16 (2002), 67--78.
  24. An estimate of the gap of spectrum of Schr\"odinger operators which generate hyperbounded semigroups, J. Funct. Anal. Vol.185 (2001) no.2, 474--526.
  25. On a certain semiclassical problem on Wiener spaces, Publ.Res.Inst.Math.Sci. Vol.39 (2003), no.2, 365--392.
  26. Semiclassical limit of the lowest eigenvalue of a Schr\"odinger operator on a Wiener space, J. Funct. Anal. 203 (2003), no.2, 401--424.
  27. Witten Laplacian on pinned path group and its expected semiclassical behavior, IDAQP, Vol.6, No.supp01,(September 2003) 103--114.
  28. Weak Poincare inequalities on domains defined by Brownian rough paths, The Annals of Probability, 2004, Vol.32, No.4, 3116--3137.
  29. Precise Gaussian estimates of heat kernels on asymptotically flat Riemannian manifolds with poles, in "Recent developments in stochastic analysis and related topics", Proceedings of the First Sino-German conference on stochatsic analysis (2002), 1--19, (2004).
  30. Semi-classical limit of the bottom of spectrum of a Schr\"odinger operator on a path space over a compact Riemannian manifold, J. Funct. Anal. Volume 251, Issue 1, 59--121, (2007).
  31. Hadamard's variation and Poincar\'e's lemma on a certain non-convex domain, Proceedings of RIMS Workshop on Stochastic Analysis and Applications, RIMS Kokyuroku Bessatsu, B6, 1--14, (2008).
  32. Log-Sobolev inequalities with potential functions on pinned path groups, the special volume for Leonard Gross's 77 birthday, Communications on Stochastic Analysis, Vol.2, No.1, April, 2008.
  33. Semi-classical limit of the lowest eigenvalue of a Schr\"odinger operator on a Wiener space : II.$P(\phi)_2$-model on a finite volume, J. Funct. Anal. Vol. 256 (2009) no.10, 3342--3367.
  34. Semi-classical limit of the lowest eigenvalue of a Schr\"odinger operator on a Wiener space: I.Unbounded one particle Hamiltonians, in "From probability to geometry (I) Volume in honor of the 60th Birthday of Jean-Michel Bismut", Asterisque, Vol 327, 2009.
  35. Rough path analysis: An introduction, Advanced Studies in Pure Mathematics 57,2010 Probabilistic Approach to Geometry, 1-28.
  36. COH formula and Dirichlet Laplacians on small domains of pinned path spaces, in the proceedings of the workshop "Concentration, Functional Inequalities, and Isoperimetry", Contemporary Mathematics, 2011, Volume 545, 1--12.
  37. Vanishing of one-dimensional L^2 cohomologies of loop groups, J.Funct.Anal. Vol. 261 (2011), Isuue 8, 2164--2213.
  38. Semiclassical limit of Schrodiner operators in infinite dimensional spaces (Japanese), Sugaku 64 (2012), no.3, 278--303.
  39. Tunneling for spatially cut-off $P(\phi)_2$-Hamiltonians, J.Funct.Anal. Vol 263 no.9 (2012), 2689--2753.
  40. Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces, (with Kosuke Sasaki), Stochastic Process. Appl. Vol. 123 (2013), Issue 10, 3800-3827.
  41. Wong-Zakai approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II, Springer Proceedings in Mathematics & Statistics 100, 1--23, 2014.
  42. Reflected rough differential equations, Stochastic Processes and Their Applications, 125, no.9, (2015), 3570-3595.
  43. Asymptotics of spectral gaps on loop spaces over a class of Riemannian manifolds, Journal of Functional Analysis, 269 no.12 (2015), 3714-3764.
  44. The rates of the Lp-convergence of the Euler-Maruyama and Wong-Zakai approximations of path-dependent stochastic differential equations under the Lipschitz condition, (with Takanori Kikuchi and Seiichiro Kusuoka), Tohoku Math. J. (2) 70 (2018), no. 1, 65--95.
  45. Error analysis for approximations to one-dimensional SDEs via the perturbation method, (with Nobuaki Naganuma), Osaka J. Math. 57 (2020), no. 2, 381--424.
  46. Rough differential equations containing path-dependent bounded variation terms, Journal of Theoretical Probability, published online March 08, 2024, https://doi.org/10.1007/s10959-024-0131.

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