An ergodic control problem arising from the principal eigenfunction of an elliptic operator

Alain BENSOUSSAN; Hideo NAGAI

doi:10.2969/jmsj/04310049

Alain BENSOUSSAN, Hideo NAGAI

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ジャーナルフリー

1991 年 43 巻 1 号 p. 49-65

DOI https://doi.org/10.2969/jmsj/04310049

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Published: 1991 Received: 1989/01/09 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) S. Albeverio, R. Høeph-Krohn and L. Streit, Energy forms, Hamiltonians and distorted Brownian paths, J. Math, Phys., 18 (1977), 907-917.
2) A. Bensoussan, Pertubation methods in optimal control, Gauthier-Villars, Paris, 1988.
3) A. Bensoussan and J. Frehse, On Bellman equations of ergodic type with quadratic growth Halmitonian, Contributions to Modern Calculus of Variations, Pitman Res. Notes Math. Ser., (ed. L. Cesari), 148, Longman, 1987, pp. 13-26.
4) A. Bensoussan and J. L. Lions, Impulsive control and quasi-variational inequalities, Gauthier-Villars, Paris, 1984.
5) R. Carmona, Regularity properties of Schrödinger and Dirichlet semigroups, J. Funct, Anal., 17 (1974), 227-237.
6) F. Gimbert, Problèmes de Neumann quasi-linéaires, J. Funct. Anal., 62 (1985), 65-72.
7) I. Karatzas, On a stochastic representation for the principal eigenvalue of a second order differential equation, Stochastics, 3 (1980), 305-321.
8) J. M. Lasry, Contrôle stochastique ergodique, Thèse d'état, Université Paris IX-Dauphine, 1974.
9) P. L. Lions, Quelques remarques sur les problèmes elliptiques quasi-linéaires du 2e ordre, J. Analyse Math., 45 (1985), 234-254.
10) M. Reed and B. Simon, Methods of modern mathematical physics I, II, III, IV, Academic Press, New-York, 1978.
11) B. Simon, Brownian motion, L^p properties of Schrödinger operators and the localization of binding, J. Funct. Anal., 35 (1980), 215-229.
12) B. Simon, Schrödinger semi-groups, Bull. Amer. Math. Soc., 7 (1982), 447-526.
13) C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc., 17 (1966), 611-616.

Right : [1] S. Albeverio, R. Høeph-Krohn and L. Streit, Energy forms, Hamiltonians and distorted Brownian paths, J. Math. Phys., 18 (1977), 907-917.
[2] A. Bensoussan, Pertubation methods in optimal control, Gauthier-Villars, Paris, 1988.
[3] A. Bensoussan and J. Frehse, On Bellman equations of ergodic type with quadratic growth Halmitonian, Contributions to Modern Calculus of Variations, Pitman Res. Notes Math. Ser., (ed. L. Cesari), 148, Longman, 1987, pp. 13-26.
[4] A. Bensoussan and J. L. Lions, Impulsive control and quasi-variational inequalities, Gauthier-Villars, Paris, 1984.
[5] R. Carmona, Regularity properties of Schrödinger and Dirichlet semigroups, J. Funct, Anal., 17 (1974), 227-237.
[6] F. Gimbert, Problèmes de Neumann quasi-linéaires, J. Funct. Anal., 62 (1985), 65-72.
[7] I. Karatzas, On a stochastic representation for the principal eigenvalue of a second order differential equation, Stochastics, 3 (1980), 305-321.
[8] J. M. Lasry, Contrôle stochastique ergodique, Thèse d'état, Université Paris IX-Dauphine, 1974.
[9] P. L. Lions, Quelques remarques sur les problèmes elliptiques quasi-linéaires du 2e ordre, J. Analyse Math., 45 (1985), 234-254.
[10] M. Reed and B. Simon, Methods of modern mathematical physics I, II, III, IV, Academic Press, New-York, 1978.
[11] B. Simon, Brownian motion, L^p properties of Schrödinger operators and the localization of binding, J. Funct. Anal., 35 (1980), 215-229.
[12] B. Simon, Schrödinger semi-groups, Bull. Amer. Math. Soc., 7 (1982), 447-526.
[13] C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc., 17 (1966), 611-616.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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