Kiyosi Itô's works published in English

Japanese

Kiyosi Itô's works published in English

(A) Papers

• On the Probability Distribution on a Compact Group. I (with Y. Kawada). Proc. Phys.-Math. Soc. Japan, 3rd. series 22 (1940), 977-998.[J-STAGE]
• On stochastic processes (infinitely divisible laws of probability) (Doctoral thesis). Japan. Journ. Math. XVIII (1942), 261-301.[J-STAGE]
• On the ergodicity of a certain stationary processes. Proc. Imp. Acad. Tokyo 20, 54-55.[Euclid]
• A kinematic theory of turbulence. Proc. Imp. Acad. Tokyo 20 (1944), 120-122.[Euclid]
• On the normal stationary process with no hysteresis. Proc. Imp. Acad. Tokyo 20 (1944), 199-202.[Euclid]
• A screw line in Hilbert space and its application to the probability theory. Proc. Imp. Acad. Tokyo 20 (1944), 203-209.[Euclid]
• Stochastic integral. Proc. Imp. Acad. Tokyo 20 (1944), 519-524.[Euclid]
• On Student's test. Proc. Imp. Acad. Tokyo 20 (1944), 694-700.[Euclid]
• On a stochastic integral equation. Proc. Imp. Acad. Tokyo 22 (1946), 32-35.[Euclid]
• Stochastic differential equations in a differentiable manifold. Nagoya Math. Journ. 1 (1950), 35-47.[Euclid]
• Brownian motions in a Lie group. Proc. Imp. Acad. Tokyo 26 (1950), 4-10.[Euclid]
• On stochastic differential equations. Mem. Amer. Math. Soc. 4 (1951), 1-51.[AMS]
• On a formula concerning stochastic differentials. Nagoya Math. Journ. 3 (1951), 55-65.[Euclid]
• Multiple Wiener integral. Journ. Math. Soc. Japan 3 (1951), 157-169.[Euclid]
• Stochastic differential equations in a differentiable manifold (2). Mem. Coll. Science, Univ. Kyoto, Ser. A. 28 (1953), 81-85.[Euclid]
• Stationary random distributions. Mem. Coll. Science, Univ. Kyoto, Ser. A. 28 (1953), 209-223.[Euclid]
• Complex multiple Wiener integral. Japan Journ. Math. 22 (1952), 63-86.[J-STAGE]
• Isotropic random current. Proc. Third Berkeley Symp. Math. Statististics and Probability (Univ. California, Berkeley, December 1954 and July-August 1955), Vol. II: Contributions to Probability Theory, pp. 125-132. Univ. of California Press, Berkeley, Calif., 1956.[Euclid]
• Spectral type of the shift transformation of differential processes with stationary increments. Trans. Amer. Math. Soc. 81 (1956), 253-263.[JSTOR]
• Potentials and random walk (with H. P. McKean, Jr.), Illinois Journ. Math. 4 (1960), 119-132.[Euclid]
• Wiener integral and Feynman integral. Proc. Fourth Berkeley Symp. Math. Statistics and Probability (University of California, Berkeley, June 20-July 30, 1960), Vol. II: Contributions to Probability Theory, pp. 227-238. University of California Press, Berkeley, Calif., 1961.[Euclid]
• Construction of diffusions. Actes du colloque de mathématiques réuni à l'occasion du tricentenaire de Blaise Pascal. Ann. Fac. Sci. Univ. Clermont-Ferrand 2, tome 8, Série Mathématiques, no. 2 (1962), 23-32.[NUMDAM]
• The Brownian motion and tensor fields on Riemannian manifold. Proc. Intern. Congr. Mathemat., (Stockholm) (1962), 536-539.[IMU,PDF]
• Brownian motion on a half line (with H. P. McKean, Jr.). Illinois Journ. Math. 7 (1963), 181-231.[Euclid]
• The expected number of zeros of continuous stationary Gaussian processes. Journ. Math. Kyoto Univ. 3 (1964), 207-216.[Euclid]
• TOn stationary solutions of a stochastic differential equation (with M. Nisio). Journ. Math. Kyoto Univ. 4 (1964), 1-75.[Euclid]
• Transformation of Markov processes by multiplicative functionals (with S. Watanabe). Ann. Inst. Fourier, Univ. Grenoble XV (1965), 13-30.[NUMDAM]
• The canonical modification of stochastic processes. Journ. Math. Soc. Japan 20 (1968), 130-150.[Euclid]
• On the convergence of sums of independent Banach space valued random variables (with M. Nisio). Osaka Journ. Math. 5 (1968), 35-48.[Euclid]
• Generalized uniform complex measures in the Hilbertian metric space with their application to the Feynman integral. Proc. Fifth Berkeley Symp. Math. Statististics and Probability (Univ. California, Berkeley, June 21-July 18, 1965 and December 27, 1965-January 7, 1966), (eds. L. M. Le Cam and J. Neyman), Vol.II: Contributions to Probability Theory, Part 1, pp. 145-161. Univ. California Press, Berkeley, Calif., 1967.[Euclid]
• On the oscillation functions of Gaussian processes (with M. Nisio).Math. Scand. 22 (1968) , 209-22[Online]
• Canonical measurable random functions. Proc. Int. Conf. Funct. Anal. Rel. Topics (Tokyo, 1969), pp. 369-377. Univ. of Tokyo Press, Tokyo, 1970.
• The topological support of a Gaussian measure on Hilbert space. Nagoya Math. Journ. 38 (1970), 181-183.[Euclid]
• Poisson point processes attached to Markov processes. Proc. Sixth Berkeley Symp. Math. Statistics and Probability (Univ. California, Berkeley, Calif., June 21-July 18, 1970, April 9-12, June 16-21, and July 19-22, 1971), (eds. L. M. Le Cam, J. Neyman and E. L. Scott), Vol.III: Probability Theory, pp. 225-239. Univ. California Press, Berkeley, Calif., 1972.[Euclid]
• Stochastic differentials of continuous local martingales. Stability of Stochastic Dynamical Systems (Proc. Internat. Sympos., Univ. Warwick, Coventry, 1972), pp. 1-7. Lecture Notes in Math., Vol. 294, Springer-Verlag, Berlin, 1972.[Springer]
• Stochastic integration. Vector and Operator Valued Measures and Applications (Proc. Sympos., Alta, Utah, 1972), pp. 141-148. Academic Press, New York, 1973.
• Stochastic differentials. Appl. Math. and Opt. 1 (1974), 374-381.[Springer]
• Stochastic parallel displacement. Probabilistic Methods in Differential Equations (Proc. Conf., Univ. Victoria, Victoria, B.C., 1974), pp. 1-7. Lecture Notes in Math., Vol. 451, Springer-Verlag, Berlin, 1975. [Springer]
• Stochastic calculus. International Symposium on Mathematical Problems in Theoretical Physics (Kyoto Univ., Kyoto, 1975), pp. 218-223. Lecture Notes in Physics, Vol. 39, Springer-Verlag, Berlin, 1975.[Springer]
• Extension of stochastic integrals. Proc. Int. Symp. Stochastic Differential Equations (RIMS, Kyoto Univ., Kyoto, 1976), pp. 95-109. Wiley, New York-Chichester-Brisbane, 1978.
• Introduction to stochastic differential equations (with S. Watanabe). Proc. Int. Symp. Stochastic Differential Equations (RIMS, Kyoto Univ., Kyoto, 1976), pp. i-xxx. Wiley, New York-Chichester-Brisbane, 1978.
• Continuous additive ${\cal S}'$-processes. Stochastic differential systems (Proc. IFIP-WG 7/1 Working Conf., Vilnius, 1978), pp. 143-151. Lecture Notes in Control and Information Sci., Vol. 25, Springer, Berlin-New York, 1980.[Springer]
• Stochastic Analysis in infinite dimensions. Stochastic Analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978) (eds. A. Friedman and M. Pinsky), pp. 187-197. Academic Press, New York-London, 1978.
• Infinite dimensional Ornstein-Uhlenbeck processes. Stochastic analysis, Proc. Taniguchi Internat. Symp. on Stochastic Analysis (Katata/Kyoto, 1982), pp. 197-224. North-Holland Math. Library, Vol. 32, North-Holland, Amsterdam, 1984.
• Regularization of linear random functionals (with M. Nawata). Probability Theory and Mathematical Statistics, Fourth USSR-Japan Symposium Proceedings (Tbilisi, USSR, August 23-29, 1982), (eds. J. V. Prokhorov and K. Itô), pp. 257-267. Lecture Notes in Math., Vol. 1021, Springer-Verlag, Berlin, 1983.[Springer]
• Distribution-valued processes arising from independent Brownian motions. Math. Zeit. 182 (1983), 17-33.[Springer]
• A stochastic differential equation in infinite dimensions. Conference in modern analysis and probability (New Haven, Conn., 1982), (eds. R. Beals, A. Beck, A. Bellow and A. Hajian), pp. 163-169. Contemporary Math., Vol. 26, Amer. Math. Soc., Providence, RI, 1984.[AMS]
• Malliavin's ${\cal C}^\infty$-functionals of a centered Gaussian system. IMA preprint Series, Univ. Minnesota, No 327 (1987).
• Malliavin calculus on a Segal space. Stochastic Analysis, Proc. of Japanese-French Seminar (Paris, France, June 16-19, 1987), (eds. M. Métivier and S. Watanabe), pp. 50-72. Lecture Notes in Math., Vol. 1322, Springer-Verlag, Berlin, 1988.[Springer]
• ositive generalized functions on $(\mathbf{R}^\infty, {\cal B}^\infty, N^\infty)$. White Noise Analysis, Mathematics and Applications (Biefeld, 1989), (eds. T. Hida, H.-H. Kuo, J. Potthoff and L. Streit), pp. 166-179. World Scientific Publ., River Edge, NJ, 1990.
• On Malliavin calculus. In Probability theory, Proceedings of 1989 Singapore Probability Conference, (eds. L. H. Y. Chen, K. P. Choi, K. Hu and J.-H. Lou), pp. 47-72, Walter de Gruyter, Berlin, 1992.
• An elementary approach to Malliavin fields. Asymptotic problems in probability theory: Wiener functionals and asymptotics, Proceedings of Taniguchi Symp. Sanda and Kyoto, 1990, (eds. K. D. Elworthy and N. Ikeda), pp. 35-89. Pitman Research Notes in Math. Series, Vol. 284, Longman, Sci. Tech, Harlow, 1993.
• Semigroups in probability theory. Functional analysis and related topics, Proceedings of the International Conference in Memory of Professor Kôsaku Yosida (RIMS, Kyoto Univ., July 29-August 2, 1991), (ed. H. Komatsu), pp. 69-83. Lecture Notes in Math., Vol. 1540, Springer-Verlag, Berlin, 1993.[Springer]
• On Malliavin tensor fields. Communs. Pure and Appl. Math. XLVII (1994), 377-403. (The third of five special issues dedicated to H. P. McKean, Jr.)[Wiley]
• A survey of stochastic differential equations. Nonlinear and convex analysis in economic theory, (Tokyo, 1993), pp. 119-129. Lecture Notes in Econom. and Math. Systems, Vol. 419, Springer, Berlin, 1995.[Springer]
• A measure-theoretic approach to Malliavin calculus. New Trends in Stochastic Analysis, Proc. Taniguchi Symposium (Sept. 1994, Charingworth), (eds. K. D. Elworthy, S. Kusuoka and I. Shigekawa), pp. 220-287. World Scientific Publ., River Edge, NJ, 1997.
• Memoirs of my research on stochastic analysis. Stochastic analysis and applications, pp. 1-5. Abel Symp. 2, Springer, Berlin, 2007.[Springer]
• On the occasion of the ceremonial 2006 Gauss Prize event at Kyoto University. Japan. J. Math 2 (2007), no. 1, 41-43.[Springer]

(B) Books

• Lectures on Stochastic Processes. Tata Institute for Fundamental Research, Bombay, 1961; (Second edition) Tata Institute of Fundamental Research Lectures on Mathematics and Physics Vol. 24. Distributed for the Tata Institute of Fundamental Research, Bombay; by Springer-Verlag, Berlin, 1984. iii+233 pp. ISBN: 3-540-12873-5
• Diffusion Processes and Their Sample Paths (with H. P. McKean, Jr.). Springer-Verlag, 1965; reprint of the 1974 Edition in the Springer Series of Classics in Mathematics, 1996.[Springer]
• Stochastic Processes. Lecture Notes Series, No. 16, Aarhus University, 1969.
• Introduction to Probability Theory (Translated from the Japanese by the author, Chapters I-IV). Cambridge Univ. Press, 1984.
• Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces. CBMS-NSF Reg. Conf. Ser. in Appl. Math. Vol. 47, SIAM, 1984.[SIAM]
• Stochastic processes, Lectures given at Aarhus University, Reprint of the 1969 original. Edited by O. E. Barndorff-Nielsen and K. Sato. Springer-Verlag, Berlin, 2004.[Springer]
• Essentials of Stochastic Processes (Translated from the Japanese by Y. Ito). Amer. Math. Soc., Providence, RI, 2006.