Fluctuations of Markovian systems in Kac's caricature of a Maxwellian gas

Kohei UCHIYAMA

doi:10.2969/jmsj/03530477

Kohei UCHIYAMA

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JOURNAL FREE ACCESS

1983 Volume 35 Issue 3 Pages 477-499

DOI https://doi.org/10.2969/jmsj/03530477

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Published: 1983 Received: July 08, 1981 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Billingsley, Convergence of probability measures, John Wiley, New York, 1968.
2) K. L. Chung, Markov chains with stationary transition probabilities, Springer-Verlag, Berlin, 1960.
3) W. Feller, An introduction to probability theory and its applications, Vol. I (second edition), John Wiley, New York, 1966.
4) R. A. Holley and D. W. Stroock, Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions, Publ. RIMS, Kyoto Univ., 14 (1978), 741-788.
5) M. Kac, Foundation of kinetic theory, Proc. Third Berkeley Symp. on Math. Stat. and Prob., 3 (1956), 171-197.
6) M. Kac, Some probabilistic aspects of the Boltzmann-equation, Acta Physica Austriaca, Suppl., 10 (1973), 379-400.
7) H. P. McKean, Jr., Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas, Arch. Rational Mech. Anal., 21 (1966), 343-367.
8) H. P. McKean, Jr., Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math., 28(1975), 435-455.
9) K. R. Parthasarathy, Probability measures on metric space, Academic Press, New York, 1969.
10) D. W. Stroock and S.R.S. Varadhan, Multidimensional diffusion processes, Springer-Verlag, Berlin, 1979.
11) H. Tanaka, Fluctuation theory for Kac's one-dimensional model of Maxwellian molecules, to appear in Sankhya Ser. A, 44 (1982).

Right : [1] P. Billingsley, Convergence of probability measures, John Wiley, New York, 1968.
[2] K. L. Chung, Markov chains with stationary transition probabilities, Springer-Verlag, Berlin, 1960.
[3] W. Feller, An introduction to probability theory and its applications, Vol. I (second edition), John Wiley, New York, 1966.
[4] R. A. Holley and D. W. Stroock, Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions, Publ. RIMS, Kyoto Univ., 14 (1978), 741-788.
[5] M. Kac, Foundation of kinetic theory, Proc. Third Berkeley Symp. on Math. Stat. and Prob., 3 (1956), 171-197.
[6] M. Kac, Some probabilistic aspects of the Boltzmann-equation, Acta Physica Austriaca, Suppl., 10 (1973), 379-400.
[7] H. P. McKean, Jr., Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas, Arch. Rational Mech. Anal., 21 (1966), 343-367.
[8] H. P. McKean, Jr., Fluctuations in the kinetic theory of gases, Comm. Pure Appl. Math., 28 (1975), 435-455.
[9] K. R. Parthasarathy, Probability measures on metric space, Academic Press, New York, 1969.
[10] D. W. Stroock and S. R. S. Varadhan, Multidimensional diffusion processes, Springer-Verlag, Berlin, 1979.
[11] H. Tanaka, Fluctuation theory for Kac's one-dimensional model of Maxwellian molecules, to appear in Sankhya Ser. A, 44 (1982).

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