Homogenization of cadlag processes

Matsuyo TOMISAKI

doi:10.2969/jmsj/04420281

Matsuyo TOMISAKI

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 2 Pages 281-305

DOI https://doi.org/10.2969/jmsj/04420281

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Published: 1992 Received: April 16, 1991 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) D. Aldous, Stopping times and tightness, Ann. Probab., 6 (1978), 335-340.
2) A. Bensoussan, J. L. Lions and G. C. Papanicolaou, Sur quelques phénomènes asymptotiques stationnaires, C. R. Acad. Sc. Paris, Série A, 281 (1975), 89-94.
3) M. Horie, T. Inuzuka and H. Tanaka, Homogenization of certain one-dimensional discontinuous Markov processes, Hiroshima Math. J., 7 (1977), 629-641.
4) T. Komatsu, Markov processes associated with certain integro-differential operators, Osaka J. Math., 10 (1973), 271-303.
5) T. Komatsu, On the martingale problem for generators of stable processes with perturbations, Osaka J. Math., 21 (1984), 113-132.
6) T. Komatsu, Pseudo-differential operators and Markov processes, J. Math. Soc. Japan, 36 (1984), 387-418.
7) O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, 23, Amer. Math. Soc., Providence, 1968.
8) P. A. Meyer, Les résolvantes fortement fellériennes d'après Mokobodzki, Séminaire de Probabilités II, Université de Strasbourg, Lecture Notes in Math., 51, Springer, 1968, pp. 171-174.
9) A. Negoro and M. Tsuchiya, Markov semigroups associated with one-dimensional Lévy operators-regularity and convergence-, Stochastic Methods in Biology (eds. M. Kimura et al.), Lecture Notes in Biomath., 70, Springer, 1987, pp. 185-193.
10) A. Negoro and M. Tsuchiya, Convergence and uniqueness theorems for Markov processes associated with Lévy operators, Probability Theory and Mathematical Statistics (eds. S. Watanabe and Yu. V. Prokhorov), Lecture Notes in Math., 1299, Springer, 1988, pp. 348-356.
11) A. Negoro and M. Tsuchiya, Stochastic processes and semigroups associated with degenerate Lévy generating operating operators, Stochastics and Stochastics Reports, 26 (1989), 29-61.
12) G. C. Papanicolaou, D. W. Stroock and S. R. S. Varadhan, Martingale approach to some limit theorems, Statistical Mechanics and Dynamical Systems, Univ. Conf. Turbulence (ed. D. Ruelle), Duke Univ. Math. Ser. III, 1977.
13) E. Seneta, Regular Varying Functions, Lecture Notes in Math., 508, Springer, 1976.
14) D. W. Stroock, Diffusion processes associated with Lévy generators, Z. Wahrsch. verw. Gebiete, 32 (1975). 209-244.
15) D. W. Stroock and S. R. S. Varadhan, Diffusion processes with continuous coefficients, I and II, Comm. Pure Appl. Math., 22 (1969), 345-400 and 479-530.
16) M. Tsuchiya, The Lipshits condition for coefficients of jump term of stochastic differential equations associated with decomposed Lévy measures (preprint).
17) H. Watanabe, Potential operator of a recurrent strong Feller process in the strict sense and boundary value problem, J. Math. Soc. Japan, 16 (1964), 83-95.

Right : [1] D. Aldous, Stopping times and tightness, Ann. Probab., 6 (1978), 335-340.
[2] A. Bensoussan, J. L. Lions and G. C. Papanicolaou, Sur quelques phénomènes asymptotiques stationnaires, C. R. Acad. Sc. Paris, Série A, 281 (1975), 89-94.
[3] M. Horie, T. Inuzuka and H. Tanaka, Homogenization of certain one-dimensional discontinuous Markov processes, Hiroshima Math. J., 7 (1977), 629-641.
[4] T. Komatsu, Markov processes associated with certain integro-differential operators, Osaka J. Math., 10 (1973), 271-303.
[5] T. Komatsu, On the martingale problem for generators of stable processes with perturbations, Osaka J. Math., 21 (1984), 113-132.
[6] T. Komatsu, Pseudo-differential operators and Markov processes, J. Math. Soc. Japan, 36 (1984), 387-418.
[7] O. A. Ladyzenskaja, V. A. Solonnikov and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, 23, Amer. Math. Soc., Providence, 1968.
[8] P. A. Meyer, Les résolvantes fortement fellériennes d'après Mokobodzki, Séminaire de Probabilités II, Université de Strasbourg, Lecture Notes in Math., 51, Springer, 1968, pp. 171-174.
[9] A. Negoro and M. Tsuchiya, Markov semigroups associated with one-dimensional Lévy operators-regularity and convergence-, Stochastic Methods in Biology (eds. M. Kimura et al.), Lecture Notes in Biomath., 70, Springer, 1987, pp. 185-193.
[10] A. Negoro and M. Tsuchiya, Convergence and uniqueness theorems for Markov processes associated with Lévy operators, Probability Theory and Mathematical Statistics (eds. S. Watanabe and Yu. V. Prokhorov), Lecture Notes in Math., 1299, Springer, 1988, pp. 348-356.
[11] A. Negoro and M. Tsuchiya, Stochastic processes and semigroups associated with degenerate Lévy generating operating operators, Stochastics and Stochastics Reports, 26 (1989), 29-61.
[12] G. C. Papanicolaou, D. W. Stroock and S. R. S. Varadhan, Martingale approach to some limit theorems, Statistical Mechanics and Dynamical Systems, Univ. Conf. Turbulence (ed. D. Ruelle), Duke Univ. Math. Ser. III, 1977.
[13] E. Seneta, Regular Varying Functions, Lecture Notes in Math., 508, Springer, 1976.
[14] D. W. Stroock, Diffusion processes associated with Lévy generators, Z. Wahrsch. verw. Gebiete, 32 (1975). 209-244.
[15] D. W. Stroock and S. R. S. Varadhan, Diffusion processes with continuous coefficients, I and II, Comm. Pure Appl. Math., 22 (1969), 345-400 and 479-530.
[16] M. Tsuchiya, The Lipshits condition for coefficients of jump term of stochastic differential equations associated with decomposed Lévy measures (preprint).
[17] H. Watanabe, Potential operator of a recurrent strong Feller process in the strict sense and boundary value problem, J. Math. Soc. Japan, 16 (1964), 83-95.

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