List of publications
Papers
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Euler polynomials, Bernoulli polynomials, and Lévy’s stochastic area formula,
Bull. Sci. math., 135 (2011) 684-694.
(with Nobuyuki Ikeda)
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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)
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The Itô-Nisio theorem, quadratic Wiener functionals, and 1-solitons,
Stoch. Proc. Appl., 120 (2010), 605-621. (with N. Ikeda)
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A Wiener integral approach to non-commutative harmonic oscillators,
Kyushu Jour. Math., 63-2 (2009), 347-352.
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The random walk model revisited,
Jour. Math-for-Indust., JMI2009A (2009), 1-6.
(with Takehiro Hirotsu)
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Quadratic Wiener functionals of square norms on measure
spaces, Commun. Stoch. Anal.
2 (2008), 11-26.
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The heat semigroup and kernel associated with certain
non-commutative haramonic oscillators,
Kyushu Jour. Math., 62-1 (2008), 63-68.
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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.
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On the Jacobi field approach to stochastic oscillatory
integrals with quadratic phase functions,
Kyushu Jour. Math., 61-1 (2007), 191-208.
- 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.
- Brownian sheet and reflectionless potentials , Stoch. Pro.
Appl., 116 (2) (2006), 293-309.
- 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.
- On Wiener functionals of order 2 associated with soliton solutions
of the KdV equation , J. Funct. Anal., 216 (2004), 212-229.
- Quadratic Wiener functionals, Kalman-Bucy filters, and the KdV
equation, Adv. Studies Pure Math., 41 (2004), 167--187. (with
N. Ikeda)
- Exponential decay of stochastic oscillatory integrals on classical
Wiener spaces, J. Math. Soc. Japan, 55 (2003), no.1, 59--79.
- Wiener functionals of second order and their Lévy measures,
Electron. J. Probab., 7 (2002), No. 14, 1--30. (with H. Matsumoto)
- Ground state estimations in gauge theory, Bull. Sci. Math.,
125 (2001), no. 6-7, 623--640. (with A.-B. Cruzeiro and P. Malliavin)
- Analytic functions on abstract Wiener spaces , J. Funct.
Anal., 179 (2001), no. 1, 235--250.
- Lévy's stochastic area and the principle of stationary phase
, J. Funct. Anal., 172 (2000), no. 1, 165--176.
- Stochastic oscillatory integrals with quadratic phase function and
Jacobi equations, Probab. Theory Related Fields, 114(1999), no.
3, 291--308.
- On the analyticity of stochastic flows, Osaka J. Math.,
36 (1999), no. 1, 139--148. (with A. Ishiwata)
- 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)
- Oscillatory integrals with quadratic phase function on a real
abstract Wiener space, J. Funct. Anal., 155 (1998), no. 1,
229--262. (with H. Sugita)
- On the exponential decay of oscillatory integrals on an abstract
Wiener space, J. Funct. Anal., 154 (1998), no. 2, 424--443.
- 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)
- 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)
- 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)
- Almost complex structures on path groups, in "Stochastic
analysis and applications (Powys, 1995)", 419--428, World Sci. Publ., 1996.
- On Ricci curvatures of hypersurfaces in abstract Wiener
spaces, J. Funct. Anal., 136 (1996), no. 1, 226--244.
- 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)
- A probabilistic scheme for collapse of metrics, J. Math.
Kyoto Univ., 36 (1996), no. 1, 73--92. (with Y. Ogura)
- On almost complex structures on abstract Wiener spaces,
Osaka J. Math., 33 (1996), no. 1, 189--206.
- Holomorphic functions on balls in an almost complex abstract Wiener
space, J. Math. Soc. Japan, 47 (1995), no. 4, 655--670.
- Diffusions as integral curves, or Stratonovich without Itô,
in "The Dynkin Festschrift", 333--369, Birkhauser, 1994. (with D. Stroock)
- 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)
- Pseudoconvex domains in almost complex abstract Wiener
spaces, J. Funct. Anal., 117 (1993), no. 1, 62--117. (with S.
Kusuoka)
- Dirichlet forms on separable metric spaces, in "Probability
theory and mathematical statistics (Kiev, 1991)", 324--353, World Sci. Publ.,
1992. (with I. Shigekawa)
- 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)
- 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.
- On the Šilov boundary of a pseudoconvex domain in Cn with
C2+α boundary, J. Funct. Anal., 99(1991), no. 1,
100--109.
- Stochastic flows of diffeomorphisms on an open set in Rn
, Stoch. Stoch. Rep., 28 (1989), no. 4, 301--315.
- Explosion problem for holomorphic diffusion processes and its
applications, Osaka J. Math., 26 (1989), no. 4, 931--951.
- 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.
- Conformal martingale diffusions and Shilov boundary , in
"Potential theory and its related fields", 145--156, RIMS Kyoto Univ. Kokyuro,
610, 1987. (with H. Kaneko)
- A stochastic approach to the Šilov boundary, J. Funct.
Anal., 74 (1987), no. 2, 415--429. (with H. Kaneko)
- 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)
- 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)
- Applications of Malliavin's calculus to time-dependent systems of
heat equations, Osaka J. Math., 22 (1985), no. 2, 307--320.
- Malliavin's stochastic calculus of variations for manifold-valued
Wiener functionals and its applications, Z. Wahrsch. Verw. Gebiete,
65 (1983), no. 2, 269--290.