AKIHIKO INOUE

Last Updated :2024/06/04

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Professor
Web Site
E-mail
inoue100hiroshima-u.ac.jp
Other Contact Details
1-3-1,Kagamiyama,Higashi-Hiroshima, Japan
TEL : (+81) FAX : (+81)82-424-0710

Basic Information

Major Professional Backgrounds

  • 1984/04/01, 1992/02/29, Hokkaido University, Faculty of Science, Research Associate
  • 1992/03/01, 1995/03/31, Hokkaido University, Faculty of Science, Lecturer
  • 1995/04/01, 2007/03/31, Hokkaido University, Graduate School of Science, Associate Professor
  • 2007/04/01, 2009/03/31, Hokkaido University, Graduate School of Science, Associate Professor
  • 2009/04/01, 2020/03/31, Hiroshima University, Graduate School of Science, Professor

Educational Backgrounds

  • The University of Tokyo, Graduate School, Division of Science, Department of Mathematics, Japan, 1982/04, 1984/03
  • The University of Tokyo, Faculty of Science, Department of Mathematics, Japan, 1978/04, 1982/03

Academic Degrees

  • Doctor of Science, HOKKAIDO UNIVERSITY
  • Master of Science, The University of Tokyo

Educational Activity

  • [Bachelor Degree Program] School of Science : Mathematics : Mathematics
  • [Master's Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program
  • [Doctoral Program] Graduate School of Advanced Science and Engineering : Division of Advanced Science and Engineering : Mathematics Program

In Charge of Primary Major Programs

  • Mathematics

Research Fields

  • Mathematical and physical sciences;Mathematics;Basic analysis

Research Keywords

  • Representation Theorems in Finite Prediction, Toeplitz Matrices, Stochastic Processes with Memory, Mathematical Finance, Tauberian Theorems

Affiliated Academic Societies

  • The Mathematical Society of Japan

Educational Activity

Course in Charge

  1. 2024, Liberal Arts Education Program1, 1Term, Introductory Seminar for First-Year Students
  2. 2024, Undergraduate Education, 2Term, Analysis A
  3. 2024, Undergraduate Education, 2Term, Exercises in Analysis A
  4. 2024, Undergraduate Education, 4Term, Probability and Mathematical Statistics C
  5. 2024, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  6. 2024, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  7. 2024, Graduate Education (Master's Program) , Academic Year, Probability Seminar
  8. 2024, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
  9. 2024, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  10. 2024, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  11. 2024, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
  12. 2024, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. Representation theorems in finite prediction, with applications, Sugaku Expositions, 36, 173-197, 20230814
  2. Explicit formulas for the inverses of Toeplitz matrices, with applications, Probability Theory and Related Fields, 185, 513-552, 202302
  3. Closed-form expression for finite predictor coefficients of multivariate ARMA processes, Journal of Multivariate Analysis, 176, 202003
  4. Representation theorems in finite prediction, with applications, Sugaku, 71(3), 302-324, 20190725
  5. Simple matrix representations of the orthogonal polynomials for a rational spectral density on the unit circle, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 464(2), 1366-1374, 20180815
  6. Baxter’s inequality for finite predictor coefficients of multivariate long-memory stationary processes, Bernoulli, 24(2), 1202-1232, 2018
  7. THE INTERSECTION OF PAST AND FUTURE FOR MULTIVARIATE STATIONARY PROCESSES, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 144(4), 1779-1786, 201604
  8. Rigidity for Matrix-Valued Hardy Functions, INTEGRAL EQUATIONS AND OPERATOR THEORY, 84(2), 289-300, 201602
  9. A Vasicek-Type Short Rate Model With Memory Effect, STOCHASTIC ANALYSIS AND APPLICATIONS, 33(6), 1068-1082, 20151102
  10. Prediction of fractional processes with long-range dependence, HOKKAIDO MATHEMATICAL JOURNAL, 41(2), 157-183, 201206
  11. An explicit representation of Verblunsky coefficients, STATISTICS & PROBABILITY LETTERS, 82(2), 403-410, 201202
  12. Duals of random vectors and processes with applications to prediction problems with missing values, STATISTICS & PROBABILITY LETTERS, 79(14), 1637-1646, 20090715
  13. Baxter's inequality for fractional Brownian motion-type processes with Hurst index less than 1/2, STATISTICS & PROBABILITY LETTERS, 78(17), 2889-2894, 2008
  14. AR and MA representation of partial autocorrelation functions, with applications, Probability Theory and Related Fields, 140(3), 523-551, 2008
  15. Remark on optimal investment in a market with memory, Theory of Stochastic Processes, 13(1-2), 66-76, 2007
  16. Prediction of fractional Brownian motion-type proesses, Stochastic Analysis and Applications, 641-666, 2007
  17. Optimal Long-Term Investment Model with Memory, Applied Mathematics and Optimization, 55(1), 93-122, 2007
  18. Binary market models with memory, Statistics & Probability Letters, 77(3), 256-264, 2007
  19. A prediction problem in L2(w), Proceedings of he American Mathematical Society, 135(4), 1233-1239, 2007
  20. Explicit representation of finite predictor coefficients and its applications, The Annals of Statistics, 34(2), 973-993, 2006
  21. Linear filtering of systems with memory and application to finance, Journal of Applied Mathematics and Stochastic Analysis, 2006(Article ID 53104), 1-26, 2006
  22. Financial markets with memory I: Dynamic models, Stochastic Analysis and Applications, 23(2), 275-300, 2005
  23. Financial markets with memory II: Innovation processes and expected utility maximization, Stochastic Analysis and Applications, 23(2), 301-328, 2005
  24. Prediction of fractional Brownian motion with Hurst index less than 1/2, Bulletin of the Australian Mathematical Society, 70, 321-328, 2004
  25. Partial autocorrelation functions of the fractional ARIMA processes with negative degree of differencing, Journal of Multivariate Analysis, 89(1), 135-147, 2004
  26. On the worst conditional expectation, Journal of Mathematical Analysis and Applications, 286(1), 237-247, 2003
  27. Asymptotic behavior for partial autocorrelation functions of fractional ARIMA processes, The Annals of Applied Probability, 12(4), 1471-1491, 2002
  28. Extension of the Drasin-Shea-Jordan theorem, Journal of the Mathematical Society of Japan, 52(3), 545-559, 2000
  29. Tauberian and Mercerian theorems for systems of kernels, Journal of Mathematical Analysis and Applications, 251(1), 177-197, 20001201
  30. Abelian, Tauberian, and Mercerian theorems for arithmetic sums, Journal of Mathematical Analysis and Applications, 250(2), 465-493, 20001015
  31. Asymptotics for prediction errors of stationary processes with reflection positivity, Journal of Mathematical Analysis and Applications, 250(1), 299-319, 20001001
  32. Asymptotics for the partial autocorrelation function of a stationary process, Journal d'Analyse Mathematique, 81(1), 65-109, 2000
  33. Abel-Tauber theorems for Hankel and Fourier transforms and a problem of Boas, Hokkaido Mathematical Journal, 28(3), 577-596, 1999
  34. On the asymptotic behavior of the prediction error of a stationary process, Trends in Probability and Related Analysis (Taipei, 1998), 207-218, 1999
  35. Ratio Mercerian theorems with applications to Hankel and Fourier transforms, Proceedings of the London Mathematical Society, 79(3), 626-648, 1999
  36. An Abel-Tauber theorem for Hankel transforms, Trends in probability and related analysis (Taipei, 1996), 83-90, 1997
  37. The Drasin-Shea-Jordan theorem for Fourier and Hankel transforms, The Quarterly Journal of Mathematics, 48(3), 279-307, 1997
  38. Regularly varying correlation functions and KMO-Langevin equations, Hokkaido Mathematical Journal, 26(2), 457-482, 1997
  39. Abel-Tauber theorems for Fourier-Stieltjes coefficients, Journal of Mathematical Analysis and Applications, 211(2), 460-480, 19970715
  40. An Abel-Tauber theorem for Fourier sine transforms, Journal of mathematical sciences, the University of Tokyo, 2(2), 303-309, 1995
  41. On Abel-Tauber theorems for Fourier cosine transforms, Journal of Mathematical Analysis and Applications, 196(2), 764-776, 19951201
  42. The theory of KM_2O-Langevin equations and applications to data analysis (II) : Causal analysis (I), Nagoya mathematical journal, 134, 1-28, 1994
  43. On the equations of stationary processes with divergent diffusion coefficients, Journal of the Faculty of Science. University of Tokyo. Section IA. Mathematics, 40, 307-336, 1993
  44. On the exponential decay of the correlation functions for KMO-Langevin equations, Japanese journal of mathematics. New series, 18(1), 13-24, 1992
  45. The Alder-Wainwright effect for stationary processes with reflection positivity. II, Osaka Journal of Mathematics, 28(3), 537-561, 1991
  46. The Alder-Wainwright effect for stationary processes with reflection positivity, Journal of the Mathematical Society of Japan, 43(3), 515-526, 1991
  47. Path integral for diffusion equations, Hokkaido Mathematical Journal, 15(1), 71-99, 1986

Publications such as books

  1. 2014, Mathematics for Finance and Insurance, Iwanami, 2014, Scholarly Book, Joint work, Akihiko Inoue; Yumiharu Nakano; Kei Fukuda, 460
  2. 2004, Have fun with mathematics, 2004, Book(general), 113~124