Bibliography of Kiyosi Itô

1942

On stochastic processes (infinitely divisible laws of probability) (Doctoral thesis). Japan Journ. Math. XVIII, 261-301.

1942

Differential equations determining a Markoff process (original Japanese: Zenkoku Sizyo Sugaku Danwakai-si). Journ. Pan-Japan Math. Coll. No.1077.

1943

Foundation of Probability Theory (in Japanese), Iwanami. Tokyo.

1944

On the ergodicity of certain stationary processes. In: Proc. Imp. Acad. Tokyo 20, 54-55.

1944

A kinematic theory of turbulence. In: Proc. Imp. Acad. Tokyo 20, 120-122.

1944

On the normal stationary process with no hysteresis. In: Proc. Imp. Acad. Tokyo 20, 199-202.

1944

A screw line in Hilbert space and its application to the probability theory. Proc. Imp. Acad. Tokyo 20, 203-209.

1944

Stochastic integral. In: Proc. Imp. Acad. Tokyo 20, 519-524.

1944

On Student's test. Proc. Imp. Acad. Tokyo 20, 694-700.

1946

On a stochastic integral equation. In: Proc. Imp. Acad. Tokyo 22, 32-35.

1950

Stochastic differential equations in a differentiable manifold. Nagoya Math. Joum. 1, 35-47.

1950

Brownian motions in a Lie group. In: Proc. Imp. Acad. Tokyo 26, 4-10.

1951

On stochastic differential equations. Mem. Amer. Math. Soc. 4, 1-51.

1951

On a formula concerning stochastic differentials. Nagoya Math. Joum.3, 55-65.

1951

Multiple Wiener integral. Journ. Math. Soc. Japan 3, 157-169.

1952

Complex multiple Wiener integral. Japan Journ. Math. 22, 63-86.

1952

Probability Theory (in Japanese), Iwanami, Tokyo.

1953

Stochastic differential equations in a differentiable manifold (2). Mem. Coll. Science, Univ. Kyoto, Ser. A., 28, 81-85.

1953

Stationary random distributions. Mem. Coll. Scien.ce, Univ. Kyoto, Ser.A., 28, 209-223.

1956

Isotropic random current. In: Proc. Third Berkeley Symp. Math. Statist. Prob. II, 125-132.

1956

Spectral type of the shift transformation of differential processes with stationary increments. Trans. Amer. Math. Soc. 81, 253-263.

1957

Stochastic Processes I, II (in Japanese), Iwanami Series of Modern Applied Mathematics A. 13, I, 11, Iwanami, Tokyo. (Russian translation by A.D. Wentzel 1960 (Part I), 1963 (Part II); English translation by Y. Ito 2006, Essentials of Stochastic Processes, American Mathematical Society)

1960

Lectures on Stochastic Processes, Tata Institute of Fundamental Research, Bombay.

1960

Potentials and random walk (with H. P. McKean, Jr.). Illinois Journ. Math. 4, 119-132.

1960

Wiener integral and Feynman integral. In: Proc. Fourth Berkeley Symp. Math. Statist. Prob. II, 227-238.

1962

Construction of diffusions. Ann. Fac. Sci. Univ. Clermont 2, 23-32.

1962

The Brownian motion and tensor fields on Riemannian manifold. In: Proc. Intern. Congr. Mathemat. (Stockholm), 536-539.

1963

Brownian motion on a half line (with H. P. McKean, Jr.). Illinois Journ. Math. 7, 181-231.

1964

The expected number of zeros of continuous stationary Gaussian processes. Journ. Math. Kyoto Univ. 3, 207-216.

1964

On stationary solutions of a stochastic differential equation (with M. Nisio). Journ. Math. Kyoto Univ. 4, 1-75 (1964).

1965

Transformation of Markov processes by multiplicative functionals (with S. Watanabe). Ann. Inst. Fourier, Univ. Grenoble XV, 13-30.

1965

Generalized uniform complex measures in the Hilbertian metric space with their application to the Feynman integral. In: Proc. Fifth Berkeley Symp. Math. Statist. Prob. II, 145-161.

1965

Diffusion Processes and Their Sample Paths (with H. P. McKean, Jr.), Springer; reprint of the 1974 Edition in the Springer Series of Classics in. Mathematics, 1996.

1968

The canonical modification of stochastic processes. Journ. Math. Soc. Japan 20, 130-150.

1968

On the convergence of sums of independent Banach space valued random variables. (with M. Nisio). Osaka Journ. Math. 5, 35-48.

1968

On the oscillation functions of Gaussian processes (with M. Nisio). Math. Scand. 22, 209-223.

1969

Aarhus Lecture Notes on Stochastic Processes, Lecture Notes Series 16, Aarhus University, Denmark. (Published 2004, Springer Verlag, eds. O. Barndorff-Nielsen and K. Sato)

1969

Canonical measurable random functions. In: Proc. Int. Conf. Funct. Anal. Rel. Topics (Tokyo), 369-377.

1970

The topological support of a Gaussian measure on Hilbert space. Nagoya Math. Journ. 38, 181-183.

1970

Poisson point processes attached to Markov processes. In: Proc. Sixth Berkeley Symp. Math. Statist. Prob. III, 225-239.

1972

Stochastic differentials of continuous local martingales. In: Stability of Stochastic Dynamical Systems. (Lecture Notes in Mathematics 294), Springer-Verlag, Berlin, 1-7.

1973

Stochastic integration. In: Vector and Operator Valued Measures and Applications, Academic Press, New York, 141-148.

1974

Stochastic differentials, Appl. Math. and Opt. 1, 374-381.

1975

Stochastic parallel displacement. In: Probabilistic Methods in Differential Equations (Lecture Notes in Mathematics 451), Springer-Verlag, Berlin, 1-7.

1975

Stochastic calculus. In: Mathematical Prob1ems in Physics (Lecture Notes in Physics 39), Springer-Verlag, 218-223.

1976

Extension of stochastic integrals. In: Proc. Int. Symp. Stochastic Differential Equations (Kyoto) 95-109.

1976

Introduction to stochastic differential equations (with S. Watanabe). In: Proc. Int. Symp. Stochastic Differential Equations (Kyoto), i-xxx.

1978

Stochastic analysis in infinite dimensions. In: Stochastic Analysis (A. Friedman and M. Pinsky, eds.), Academic Press, New York, 187-197.

1978

Probability Theory (in Japanese), Iwanami Series of Fundamental Mathematics Analysis (I) vii, Iwanami, Tokyo, revised 1983.

1980

Continuous additive S'-processes. Lect. Notes in Control and Inform. Sci. 25, Springer, New York, 36-46.

1982

Infinite dimensional Ornstein-Uhlenbeck processes. In: Taniguchi Symp. SA, Katata, 197-224.

1982

Regularization of linear random functionals (with M. Nawata). In Probability Theory and Mathematical Statistics, Fourth USSR-Japan Symposium Proceedings, 1982 (Lecture Notes in Mathematics 1021), Springer-Verlag, Berlin, 257-267.

1983

Distribution-valued processes arising from independent Brownian motions. .Math. Zeit. 182, 17-33.

1984

A stochastic differential equation in infinite dimensions. In: Contemporory Math.26, 163-169.

1984

Introduction to Probability Theory (English translation of Chapters I-IV of 1978 Probability Theory, Iwanami) Cambridge University Press.

1984

Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces. (CBMS-NSF Reg. Conf. Ser. in Appl. Math. 47) SIAM.

1985

Editor, Iwanami Sūgaku Ziten, 3rd edition, Iwanami, Tokyo.

1987

Editor, Encyclopedic Dictionary of Mathematics, second edition, Vol I-IV, MIT Press, Cambridge, Mass., and London, England. (English translation of Iwanami Sūgaku Ziten, 3rd edition, 1985)

1987

Kiyosi Itô, Selected Papers (eds. D. W. Stroock and S. R. S. Varadhan) Springer-Verlag.

1987

Malliavin's C-functionals of a centered Gaussian system. IMA Preprint Series, Univ. Minnesota, No 327.

1988

Malliavin calculus on a Segal space. In: Stochastic Analysis, Proc. of Japanese-French Seminar, Paris, 1987, (eds. M. Métivier and S. Watanabe), Lecture Notes in Mathematics 1322, Springer-Verlag, Berlin, 50-72.

1990

Positive generalized functions on (R, B, N). In: White Noise Analysis Mathematics and Applications, (eds. T. Hida, H.-H. Kuo, J. Potthoff and L. Streit), World Scientific, 166-179.

1992

On Malliavin calculus. In: Proceedings of 1989 Singapore Probability Conference, (eds. L. H. Y. Chen, K. P. Choi, K. Hu and J.-H. Lou), Walter de Gruyter, 47-72.

1993

An elementary approach to Malliavin fields, in Asymptotic problems in probability theory: Wiener functionals and asymptotics, Proceedings of Taniguchi Symp. Sanda and Kyoto. 1990, (eds. K. D. Elworthy and N. Ikeda), Pitman Research Notes in Math. Series 284, Longman, 35-89.

1993

Semigroups in probability theory. In: Functional analysis and related topics. Proceedings of the International Conference in Memory of Professor Kôsaku Yosida. RIMS, Kyoto Univ. 1991, (ed. H. Komatsu), Lecture Notes in Mathematics 1540, Springer-Verlag, Berlin, 69-83.

1994

On Malliavin tensor fields. Communs. Pure and Appl. Math. XLVII, 377-403 (1994). (The third of five special issues dedicated to Henry McKean.)

1997

A measure-theoretic approach to Malliavin calculus. In: New Trends in Stochastic Analysis, Proc. Taniguchi Symposium, Sept. 1994, Charingworth, (eds. K. D. Elworthy, S. Kusuoka and I. Shigekawa), World Scientific, 220-287.

2004

Stochastic Processes (eds. O. Barndorff-Nielsen and K. Sato), Springer-Verlag (originally published as Lecture Notes from Aarhus University 1969).

2006

Essentials of Stochastic Processes (translated by Yuji Ito, 1957 Stochastic Processes, Iwanami), Translations of Mathematical Monographs, vol. 231, American Mathematical Society.

   
 

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Research Institute for Mathematical Sciences
Kyoto University