Masatoshi Fukushima

Professor Emeritus, Osaka University
Doctor of Science (Mathematics)
Furuedai 3-14-1-512 Suita, Osaka 565-0874 Japan

Masatoshi Fukushima: Selecta

Edited by Niels Jacob, Yoichi Oshima and Masayoshi Takeda
De Gruyter, Berlin/New York, 2010


  1. Recurrent Dirichlet forms and Markov property of associated Gaussian fields
    (with Yoichi Oshima) (PDF)
  2. Logarithmic and linear potentials of signed measures and Markov property of associated Gaussian fields (PDF)
  3. Liouville property of harmonic functions with finite energy for Dirichlet forms (PDF)

Publications since 2000

  1. Stochastic Komatu-Loewner evolutions and BMD domain constant, to appear in Stochastic Processes and their Applications
    (with Zhen-Qing Chen)
  2. Reflections at infinity of time changed RBMs on a domain with Liouville branches, to appear in Journal of Mathematical Society of Japan
    (with Zhen-Qing Chen) (PDF)
  3. Stochastic Komatu-Loewner evolutions and SLEs, Stochastic Processes and their Applications 127 (2017), 2068-2087
    (with Zhen-Qing Chen and Hiroyuki Suzuki) (PDF)
  4. Chordal Komatu-Loewner equation and Brownian motion with darning in multiply connected domains, Trans. Amer. Math. Soc. 368 (2016), 4065-4114
    (with Zhen-Qing Chen and Steffen Rohde) (PDF)
  5. One-point reflection, Stochastic Processes and their Applications, 125 (2015), 1368-1393 (with Zhen-Qing Chen) (PDF)
  6. On Villat's kernels and BMD Schwarz kernels in Komatu-Loewner equations, in: Stochastic Analysis and Applications 2014, (Eds) D. Crisan; B. Hambly; T. Zariphopoulous, Springer Proceedings in Mathematics and Statistics, Vol. 100, 2014, pp327-348
    (with Hiroshi Kaneko) (PDF)
  7. On general boundary conditions for one-dimensional diffusions with symmetry, J. Math. Soc. Japan 66 (2014), 289-316 (PDF)
  8. A localization formula in Dirichlet form theory, Proc. Amer. Math. Soc. 140(2012), 1815-1822 (with Z.-Q. Chen)
  9. Jump-type Hunt processes generated by lower bounded semi-Dirichlet forms, Ann. Probab. 40(2012), 858-889 (with T. Uemura) (PDF)
  10. From one dimensional diffusions to symmetric Markov processes, Stochastic Processes and their Applications, 120(2010), 590-604
  11. On extended Dirichlet spaces and the space of BL functions, in 'Potential Theory and Stochastics in Albac', Eds. D.Bakry, L.Beznea, N. Boboc, M.Roeckner, Theta Foundation, Bucharest, AMS International Book Series, 2009. pp101-110 (PDF of preprint)
  12. On unique extension of time changed reflecting Brownian motions, Ann. Inst. Henri Poincare, Probab. Statist. 45 (2009), 864-875 (with Z.Q. Chen) (PDF)
  13. Flux and lateral conditions for symmetric Markov processes, Potential Analysis 29(2008), 241-269 (with Z.Q. Chen)
  14. One-point extensions of Markov processes by darning, Probab.Theory Relat. Fields, 141(2008), 61-112 (with Z.Q. Chen)
  15. On Feller's boundary problem for Markov processes in weak duality, J.Funct.Anal. 252(2007), 710-733 (with Z.Q. Chen)
  16. Extending Markov processes in weak duality by Poisson point processes of excursions, in: Stochastic Analysis and Applications, The Abel Symposium 2005 (Eds) F.E.Benth; G. Di Nunno; T. Lindstrom; B.Oksendal; T.Zhang, Springer, 2007, pp153-196 (with Z.Q. Chen and J. Ying)
  17. Entrance law, exit system and Levy system of time changed processes, Illinois J. Math. 50(2006), 269-312 (with Z.Q. Chen and J. Ying)
  18. Traces of symmetric Markov processes and their characterizations, Ann. Probab. 34(2006), 1052-1102 (with Z.Q.Chen and J.Ying) (PDF)
  19. Poisson point processes attached to symmetric diffusions, Ann. Inst. H. Poincare Probab. Statist. 41(2005),419-459 (with H. Tanaka) (PDF of preprint)
  20. On regular Dirichlet subspaces of H^1(I) and associated linear diffusions, Osaka J. Math. 42(2005), 1-15 (with X. Fang and J. Ying) (PDF of preprint)
  21. Time changes of symmetric diffusions and Feller measures, Ann. Probab. 32(2004), 3138-3166 (With P. He and J. Ying) (PDF of preprint)
  22. Function spaces and symmetric Markov processes, Advanced Studies in Pure Mathematics 41(2004), Stochastic Analysis and Related Topics, pp.75-89
  23. On spectral synthesis for contractive p-norms and Besov spaces, Potential Analysis 20(2004), 195-206 (with T. Uemura)
  24. Capacitary bounds of measures and ultracontractivity of time changed processes, J. Math. Pures. Appl. 82(2003) 553-572 (with T. Uemura)
  25. A note on regular Dirichlet subspaces, Proc. Amer.Math. Soc. 131(2003), 1607-1610 (with J. Ying)
  26. On Sobolev and capacitary inequalities for contractive Besov spaces over d-sets, Potential Analysis 18(2003), 59-77 (with T. Uemura)
  27. Dynkin games via Dirichlet forms and singular control of one-dimensional diffusions, SIAM J.on Control and Optimization, 41(2002), 682-699 (with M. Taksar) (PDF of preprint)
  28. On the space of BV functions and a related stochastic calculus in infinite dimensions, J.Functional Analysis, J. Functional Analysis, 183(2001),245-268(with M. Hino) (PDF of preprint)
  29. BV functions and distorted Ornstein Uhlenbeck processes over the abstract Wiener space, J.Functional Analysis, 174(2000), 227-249 (PDF of preprint)
  30. On limit theorems for Brownian motions on unbounded fractal sets, in 'Fractal Geometry and Stochastics II', ed. S.Graf, Birkhauser, Basel, 2000, p227-236
  31. On Ito's formulae for additive functionals of symmetric diffusion processes, in 'Stochastic Processes, Physics and Geometry: New Interplays. a volume in honor of Sergio Albeverio', eds.F. Getsztesy, CMS Conf. Proc.28(2000), Amer.Math.Soc., Providence, p201-211

Lecture Notes and Expository Writings

  1. Komatu-Loewner differential equations, to appear in Sugaku Expositions, AMS (PDF)
  2. On general boundary conditions for one-dimensional diffusions and symmetry
    MinnHoKee Lecture at Seoul National University, June 7,8, 2012 (PDF)
  3. On the works of Kiyosi Ito and stochastic analysis
    Japan J. Math. 2(2007), 45-53 (PDF)
  4. Feller's contributions to the one-dimensional diffusion theory and beyond, William Feller Selected Papers II, Edited by Rene L. Schilling, Zoran Vondracek, Wojbor A. Woyczynski, Springer, 2015, pp63-76 (PDF)
  5. Decompositions of symmetric diffusion processes and related topics in analysis, Sugaku Expositions AMS, vol.14, No.1, 2001 (PDF)


  1. Zhen-Qing Chen and Masatoshi Fukushima
    Symmetric Markov Processes, Time Changes, and Boundary Theory
    Pinceton Univesrity Press, Princeton and Oxford, 2012
  2. Masatoshi Fukushima, Yoichi Oshima and Masayoshi Takeda
    Dirichlet Forms and Symmetric Markov Processes
    De Gruyter, Berlin/New York, 1994, 2nd Edition 2011
  3. Masatoshi Fukushima
    Dirichlet Forms and Markov Processes
    North-Holland/Kodansha, 1980

Festschrift Masatoshi Fukushima

in honor of Masatoshi Fukushima's Sanju,
Edited by Zhen-Qing Chen, Niels Jacob, Masayoshi Takeda, Toshihiro Uemura
World Scientific, 2015

Short Biography

Born in 1935 in Osaka.
In the period 1959-61, he was a graduate student at Kyoto University.
His first academic position was a research associate of Nagoya University.
He had been a Professor of Osaka University from 1977 until retirement in 1998.
He then moved to Kansai University until retirement there in 2006.