List of publications


Papers

  1. Euler polynomials, Bernoulli polynomials, and Lévy’s stochastic area formula, Bull. Sci. math., 135 (2011) 684-694. (with Nobuyuki Ikeda)
  2. Anderson-Darling test and the Malliavin calculus, Jour. Math-for-Indust., JMI2009A (2011), 73-78. (with Takehiro Hirotsu, Hiroki Kondo, Shingo Saito, Takuya Sato, and Tatsushi Tanaka)
  3. The Itô-Nisio theorem, quadratic Wiener functionals, and 1-solitons, Stoch. Proc. Appl., 120 (2010), 605-621. (with N. Ikeda)
  4. A Wiener integral approach to non-commutative harmonic oscillators, Kyushu Jour. Math., 63-2 (2009), 347-352.
  5. The random walk model revisited, Jour. Math-for-Indust., JMI2009A (2009), 1-6. (with Takehiro Hirotsu)
  6. Quadratic Wiener functionals of square norms on measure spaces, Commun. Stoch. Anal. 2 (2008), 11-26.
  7. The heat semigroup and kernel associated with certain non-commutative haramonic oscillators, Kyushu Jour. Math., 62-1 (2008), 63-68.
  8. Stochastic calculus and the KdV equation , in "Stochastic Analysis and Partial Differential equations", eds. G.-Q. Chen, E. Hsu, and M. Pinsky, Contemp. Math., 429 (2007), 245-256.
  9. On the Jacobi field approach to stochastic oscillatory integrals with quadratic phase functions, Kyushu Jour. Math., 61-1 (2007), 191-208.
  10. On the Quadratic Wiener Functional Associated with the Malliavin Derivative of the Square Norm of Brownian Sample Path on Interval , Electron. Comm. Probab. 11 (2006), 1-10.
  11. Brownian sheet and reflectionless potentials , Stoch. Pro. Appl., 116 (2) (2006), 293-309.
  12. Stochastic oscillatory integrals: Asymptotics and exact expressions for quadratic phase function , in "Stochstic analysis and mathematical physics (SAMP/ANESTOC 2002)", ed. R. Rebolledo, J. Resende, and J.-C. Zambrini, pp. 165-181, World Scientific, 2004.
  13. On Wiener functionals of order 2 associated with soliton solutions of the KdV equation , J. Funct. Anal., 216 (2004), 212-229.
  14. Quadratic Wiener functionals, Kalman-Bucy filters, and the KdV equation, Adv. Studies Pure Math., 41 (2004), 167--187. (with N. Ikeda)
  15. Exponential decay of stochastic oscillatory integrals on classical Wiener spaces, J. Math. Soc. Japan, 55 (2003), no.1, 59--79.
  16. Wiener functionals of second order and their Lévy measures, Electron. J. Probab., 7 (2002), No. 14, 1--30. (with H. Matsumoto)
  17. Ground state estimations in gauge theory, Bull. Sci. Math., 125 (2001), no. 6-7, 623--640. (with A.-B. Cruzeiro and P. Malliavin)
  18. Analytic functions on abstract Wiener spaces , J. Funct. Anal., 179 (2001), no. 1, 235--250.
  19. Lévy's stochastic area and the principle of stationary phase , J. Funct. Anal., 172 (2000), no. 1, 165--176.
  20. Stochastic oscillatory integrals with quadratic phase function and Jacobi equations, Probab. Theory Related Fields, 114(1999), no. 3, 291--308.
  21. On the analyticity of stochastic flows, Osaka J. Math., 36 (1999), no. 1, 139--148. (with A. Ishiwata)
  22. A remark on stochastic oscillatory integrals with respect to a pinned Wiener measure, Kyushu J. Math., 53 (1999), no. 1, 151--162. (with H. Sugita)
  23. Oscillatory integrals with quadratic phase function on a real abstract Wiener space, J. Funct. Anal., 155 (1998), no. 1, 229--262. (with H. Sugita)
  24. On the exponential decay of oscillatory integrals on an abstract Wiener space, J. Funct. Anal., 154 (1998), no. 2, 424--443.
  25. Analytic functions, Cauchy formula, and stationary phase on a real abstract Wiener space, J. Funct. Anal., 143 (1997), no. 2, 470--528. (with P. Malliavin)
  26. Diffusions as integral curves on manifolds and Lie groups, in "Probability theory and mathematical statistics (St. Petersburg, 1993)", 219--226, Gordon and Breach, 1996. (with D.W. Stroock)
  27. A Kähler metric on a based loop group and a covariant differentiation, in "Ito's stochastic calculus and probability theory", 327--346, Springer, 1996. (with I. Shigekawa)
  28. Almost complex structures on path groups, in "Stochastic analysis and applications (Powys, 1995)", 419--428, World Sci. Publ., 1996.
  29. On Ricci curvatures of hypersurfaces in abstract Wiener spaces, J. Funct. Anal., 136 (1996), no. 1, 226--244.
  30. Extension holomorphe des fonctionnelles analytiques définies sur un espace de Wiener réel, formule de Cauchy, phase stationnaire, C. R. Acad. Sci. Paris Ser. I Math., 322 (1996), no. 3, 261--265. (with P. Malliavin)
  31. A probabilistic scheme for collapse of metrics, J. Math. Kyoto Univ., 36 (1996), no. 1, 73--92. (with Y. Ogura)
  32. On almost complex structures on abstract Wiener spaces, Osaka J. Math., 33 (1996), no. 1, 189--206.
  33. Holomorphic functions on balls in an almost complex abstract Wiener space, J. Math. Soc. Japan, 47 (1995), no. 4, 655--670.
  34. Diffusions as integral curves, or Stratonovich without Itô, in "The Dynkin Festschrift", 333--369, Birkhauser, 1994. (with D. Stroock)
  35. Dirichlet forms on infinite-dimensional space and related topics, Sugaku Expositions, 7 (1994), no. 2, 209--227 (Original Japanese version; Sugaku 45 (1993), no. 2, 141--156). (with I. Shigekawa)
  36. Pseudoconvex domains in almost complex abstract Wiener spaces, J. Funct. Anal., 117 (1993), no. 1, 62--117. (with S. Kusuoka)
  37. Dirichlet forms on separable metric spaces, in "Probability theory and mathematical statistics (Kiev, 1991)", 324--353, World Sci. Publ., 1992. (with I. Shigekawa)
  38. On the closable parts of pre-Dirichlet forms and the fine supports of underlying measures, Osaka J. Math., 28 (1991), no. 3, 517--535. (with M. Fukushima and K. Sato)
  39. The explosion property of holomorphic diffusion processes on a bounded pseudoconvex domain in Cn and its applications, J. Math. Kyoto Univ., 31 (1991), no. 2, 573--582.
  40. On the Šilov boundary of a pseudoconvex domain in Cn with C2+α boundary, J. Funct. Anal., 99(1991), no. 1, 100--109.
  41. Stochastic flows of diffeomorphisms on an open set in Rn , Stoch. Stoch. Rep., 28 (1989), no. 4, 301--315.
  42. Explosion problem for holomorphic diffusion processes and its applications, Osaka J. Math., 26 (1989), no. 4, 931--951.
  43. Kähler diffusion processes associated with the Bergman metric and domains of holomorphy, Proc. Japan Acad. Ser. A, Math. Sci., 64 (1988), no. 6, 184--186.
  44. Conformal martingale diffusions and Shilov boundary , in "Potential theory and its related fields", 145--156, RIMS Kyoto Univ. Kokyuro, 610, 1987. (with H. Kaneko)
  45. A stochastic approach to the Šilov boundary, J. Funct. Anal., 74 (1987), no. 2, 415--429. (with H. Kaneko)
  46. Regular points for the first boundary value problem associated with degenerate elliptic operators, in "Probability theory and harmonic analysis (Cleveland, Ohio, 1983)", 183--194, Dekker, New York, 1986. (with D.W. Stroock)
  47. The Malliavin calculus and long time asymptotics of certain Wiener integrals, in "Miniconference on linear analysis and function spaces (Canberra, 1984)", 46--113, Proc. Centre Math. Anal. Austral. Nat. Univ., 9, 1985. (with N. Ikeda and I. Shigekawa)
  48. Applications of Malliavin's calculus to time-dependent systems of heat equations, Osaka J. Math., 22 (1985), no. 2, 307--320.
  49. Malliavin's stochastic calculus of variations for manifold-valued Wiener functionals and its applications, Z. Wahrsch. Verw. Gebiete, 65 (1983), no. 2, 269--290.