A decomposition of Markov processes

Keniti SATO

doi:10.2969/jmsj/01730219

Keniti SATO

Author information

JOURNAL FREE ACCESS

1965 Volume 17 Issue 3 Pages 219-243

DOI https://doi.org/10.2969/jmsj/01730219

Details

Published: 1965 Received: January 07, 1965 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
Correction information
Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) W. Feller, On second order differential operators, Ann. of Math., 61 (1955), 90-105.
2) M. Fukushima, M. Nagasawa and K. Sato, Transformations of Markov processes and boundary problems, Seminar on Probability 16, 1963 (mimeographed note in Japanese).
3) G. A. Hunt, Markoff processes and potentials, Illinois J. Math., 1 (1957), 44-93, 316-369 and 2 (1958), 151-213.
4) N. Ikeda, M. Nagasawa and K. Sato, A time reversion of Markov processes with killing, Kodai Math. Sem. Rep., 16 (1964), 88-97.
5) K. Ito, Lectures on stochastic processes, Tata Institute of Fundamental Research, Bombay, 1961.
6) S. Ito, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math., 27 (1957), 55-102.
7) P.-A. Meyer, Fonctionnelles multiplicatives et additives de Markov, Ann. Inst. Fourier (Grenoble), 12 (1962), 125-230.
8) M. Motoo, The sweeping-out of additive functionals and processes on the boundary, Ann. Inst. Statist. Math., 16 (1964), 317-345.
9) M. Nagasawa, Time reversions of Markov processes, Nagoya Math. J. 24 (1964), 177-204.
10) M. Nagasawa and K. Sato, Some theorems on time change and killing of Markov processes, Kodai Math. Sem. Rep., 15 (1963), 195-219.
11) J. Neveu, Une généralisation des processus à accroissements positifs independents, Abh. Math. Sem. Univ. Hamburg, 25 (1961), 36-61.
12) K. Sato, Time change and killing for multi-dimensional reflecting diffusion, Proc. Japan Acad., 39 (1963), 69-73.
13) K. Sato and H. Tanaka, Local times on the boundary for multi-dimensional reflecting diffusion, Proc. Japan Acad., 38 (1962), 699-702.
14) M. G. Šur, Continuous additive functionals of Markov processes and excessive functions, Dokl. Akad. Nauk SSSR, 137 (1961), 800-803 (in Russian).
15) T. Ueno, The Brownian motion satisfying Wentzell's boundary condition, Bull. Inst. Internat. Statist., 38 (1961), 613-624.
16) T. Ueno, The diffusion satisfying Wentzell's boundary condition and the Markov process on the boundary, Proc. Japan Acad., 36 (1960), 533-538 and 625-629.
17) V. A. Volkonskii, Additive functionals of Markov processes, Trudy Moskov. Mat. Obšc., 9 (1960), 143-189 (in Russian).

Right : [1] W. Feller, On second order differential operators, Ann. of Math., 61 (1955), 90-105.
[2] M. Fukushima, M. Nagasawa and K. Sato, Transformations of Markov processes and boundary problems, Seminar on Probability 16, 1963 (mimeographed note in Japanese).
[3] G. A. Hunt, Markoff processes and potentials, Illinois J. Math., 1 (1957), 44-93, 316-369 and 2 (1958), 151-213.
[4] N. Ikeda, M. Nagasawa and K. Sato, A time reversion of Markov processes with killing, Kodai Math. Sem. Rep., 16 (1964), 88-97.
[5] K. Ito, Lectures on stochastic processes, Tata Institute of Fundamental Research, Bombay, 1961.
[6] S. Ito, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math., 27 (1957), 55-102.
[7] P. -A. Meyer, Fonctionnelles multiplicatives et additives de Markov, Ann. Inst. Fourier (Grenoble), 12 (1962), 125-230.
[8] M. Motoo, The sweeping-out of additive functionals and processes on the boundary, Ann. Inst. Statist. Math., 16 (1964), 317-345.
[9] M. Nagasawa, Time reversions of Markov processes, Nagoya Math. J. 24 (1964), 177-204.
[10] M. Nagasawa and K. Sato, Some theorems on time change and killing of Markov processes, Kodai Math. Sem. Rep., 15 (1963), 195-219.
[11] J. Neveu, Une généralisation des processus à accroissements positifs independents, Abh. Math. Sem. Univ. Hamburg, 25 (1961), 36-61.
[12] K. Sato, Time change and killing for multi-dimensional reflecting diffusion, Proc. Japan Acad., 39 (1963), 69-73.
[13] K. Sato and H. Tanaka, Local times on the boundary for multi-dimensional reflecting diffusion, Proc. Japan Acad., 38 (1962), 699-702.
[14] M. G. Šur, Continuous additive functionals of Markov processes and excessive functions, Dokl. Akad. Nauk SSSR, 137 (1961), 800-803 (in Russian).
[15] T. Ueno, The Brownian motion satisfying Wentzell's boundary condition, Bull. Inst. Internat. Statist., 38 (1961), 613-624.
[16] T. Ueno, The diffusion satisfying Wentzell's boundary condition and the Markov process on the boundary, Proc. Japan Acad., 36 (1960), 533-538 and 625-629.
[17] V. A. Volkonskii, Additive functionals of Markov processes, Trudy Moskov. Mat. Obšc., 9 (1960), 143-189 (in Russian).

Date of correction: September 26, 2006 Reason for correction: - Correction: PDF FILE Details: -

Corresponding author

Correction information

Register with J-STAGE for free!