Lectures on young measure theory and its applications in economics

Rendiconti dell'Istituto di Matematica dell'Universita di Trieste

Volumn 31, Issue , 2000, Pages 1-69

  Balder, Erik J ^a  

^a UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85045524321     PISSN: 00494704     EISSN: 24648728     Source Type: Journal    
DOI: None     Document Type: Article

References (98)

1. D.J. ALDOUS, Limit threms for subsequences of arbitrarily-dependent sequences of random variables, Z. Wahrscheinlichkeitsth. Verw. Geb. 40 (1977), 59-82
2. Z. ARTSTEIN, On a variational problem, J. Math. Anal. Appl. 45 (1974), 404-415
3. Z. ARTSTEIN, A note on Fatou's lemma in several dimensions, J Math. Econom. 6 (1979), 277-282
4. R.B. ASH, Real analysis an probability, Academic Press, New York, 1972
5. J.P. AUBIN AND I. EKELAND, Applied nonlinear analysis, Wiley New York, 1984
6. R.J. AUMANN AND M. PERLES, A variational problem arising in economics, J. Math. Anal. Appl. 11 (1965), 488-503
7. E.J. BALDER, Young measure techniques for existence of Cournot Nash-Walras equilibria, Topics on Mathematical Economics and Game Theory: Essay in honor of R.J. Aumann (M. Wooders, ed.) Fields Institute Communications no.23, American Mathemetical Society, Providence, RI, USA (1999) pp.31-39
8. E.J. BALDER, On a useful compactification for optimal control problems, J. Math. Anal. Appl. 72 (1979), 391-398
9. E.J. BALDER, Mathematical foundations of statistical decision theory: A modern viewpoint I, Preprint, Mathematical Institute, University of Utrecht, 1981
10. E.J. BALDER, Existence results without convexity conditions for general problems of optimal control with singular components, J. Math. Anal. Appl. 101 (1984), 527-539
11. E.J. BALDER, A general approach to lower semicontinuity and lower closure in optimal control theory, SIAM J. Control Opti. 22 (1984) 570-598
12. E.J. BALDER, A general denseness result for relaxe control theory Bull. Austral. Math. Soc. 30 (1984), 463-475
13. E.J. BALDER, A unifying note on Fatou's lemma in several dimensions, Math. Oper. Res. 9 (1984), 267-275
14. E.J. BALDER, An extension of Prohorov's theorem for transition probabilities with applications to infinitedimensional lower closure problems, Rend. Circ. Mat. Palermo 34 (1985), 427-447
15. E.J. BALDER, Lower closure for orientor fields by lower semicontinuity of outer integral functionals, Ann. Mat. Pura Appl. 139 (1985) no.IV, 349-360
16. E.J. BALDER, On seminormality of integral functionals an their in-grands, SIAM J. Control Optim. 24 (1986), 95-121
17. E.J. BALDER, Generalized equilibrium results for games with incomplete information, Math. Oper. Res. 13 (1988), 265-276
18. E.J. BALDER, On Prohorov's theorem for transition probabilities Analyse Convexe 19 (1989), 9.1-9.11
19. E.J. BALDER, Unusual applications of a.e. convergence, Almost Everywhere Convergence (G.A. Edgar and L. Sucheston, eds), Academi Press, New York, 1989, pp. 31-53
20. E.J. BALDER, New sequential compactness results for spaces o scalarly integrable functions, J. Math. Anal. Appl. 151 (1990), 1-16
21. E.J. BALDER, On Cournot-Nash equilibrium distributions for games with differential information and dscontinuous payoffs, Econ. 1 (1991), 339-354
22. E.J. BALDER, On equivalence of strong and weak convergence in h-spaces uner extreme point conditions, Israel J. Math. 75 (1991), 21-48
23. E.J. BALDER, Existence of optimal solutions for control and variational problems with recursive objectives, J. Math. Anal. Appl. 178 (1993), 418-437
24. E.J. BALDER, New exstence results for optimal controls in the absence of convexity: the importance of extremality, SIAM J. Control Optim. 32 (1994), 890-916
25. E.J. BALDER, A unified approach to several results involving integral of multifunctions, Set-valued Anal. 2 (1994), 63-75
26. E.J. BALDER, Lectures on Young measures, no, Cahiers de Mathematiques de la Decision, CEREMADE, Universite Paris Dauphine, Paris, 1995
27. E.J. BALDER, A unifying approach to exstence o Nash equilibria Intern. J. Game Theory 24 (1995), 79-94
28. E.J. BALDER, Comments on the existence of equilibrium istributions J. Math. Econom. 25 (1996), 307-323
29. E.J. BALDER, On the existence of optimal contract mechanisms for incomplete information principal-agent models, J. Econ. Theory 68 (1996), 133-148
30. E.J. BALDER, Consequences of denseness of Dirac Young measures J. Math. Anal. Appl. 207 (1997), 536-540
31. E.J. BALDER, An extension of the Dunford-Pettis theorem with applications to a Bocce-type oscillation restriction criterion, Preprint Department of Mathematics, University of Utrecht, 1997
32. E.J. BALDER, On the existence of Cournot-Nash equilibria in continuum games, Preprint, Department of Mathematics, University of Utrecht, 1997, JMath. Econom. (1999) no32 pp 207-215
33. E.J. BALDER, Report on the doctoral thesis of Florence Galdeano Tech. report, Departement de Mathematiques, Universite de Perpig-nan, Academie de Montpellier, 1997
34. E.J. BALDER, New fundamentals of Young measure convergence, Calculus of Variations and Optimal Control (Haifa) (A. Ioffe, S. Reich, and I. Shafrir, eds.), Chapman and Hall/CRC, 1998, Research Notes in Mathematics no. 411 (1999) pp 24-48
35. E.J. BALDER, Unifying CournotNash equilibrium existence results for continuum games, Preprint, Department of Mathematics, University of Utrecht, 1999, to appear in J.Econ.Theory
36. e-convergence by the Bocce-criterion, Studia Math. Ill (1994), 241-262
37. E.J. BALDER AND C. HESS, Fatou's lemma for multifunctions with unbounded values, Math. Oper. Res. 20 (1995), 175-188
38. E.J. BALDER AND C. HESS, Two generalizations of Komlos' theorem with lower closure-type applications, J. Convex Anal. 3 (1996), 25-44
39. E.J. BALDER AND A. RUSTICHINI, An equilibrium result for games with private information an infinitely many players, J. Econ. Theory 62 (1994), 385-393
40. J.M. BALL, A version of the fundamental theorem for young measures, PDEs and Continuum Models of Phase Transitions (M. Rascle, D. Serre, and M. Slemrod, eds.), Lecture Notes in Physics, vol. 344 SpringerVerlag, Berlin, 1984, pp. 207-215
41. R.A. BECKER, J.H. BOYD, AND B.Y. SUNG, Recursive utility and optimal capital accumulation, i. exstence, J. Econ. Theory 47 (1989) 76-100
42. H. BERLIOCCHI AND J.M. LASRY, Integrandes normales et mesures parametrees en calcul des variations ull. Soc. Math. France 101 (1973), 129-184
43. D.P BERTSEKAS AND S.E. SHREVE, Stochastic optimal control: the discrete time case, Academic Press, New York, 1978
44. P. BILLINGSLEY, Convergence of probability measures, Wiley, New York, 1968
45. p a valori in un spazio di Banach, Ann. Mat. Pura Appl. 123 (1980), no. I, 16-26
46. N. BOURBAKI, Integration, ch. IX, Hermann, Paris, 1969
47. J. BROOKS AND N. DINCULEANU, Weak compactness in spaces o Bochner integrable functions and applications, Adv. in Math. 24 (1977), 172-188
48. C. CASTAING, A propos e I'existence des sections separement mesurables et separement continues d'une multiapplication separement mesurable et separement semicontinue inferieurement Sem. Analyse Convexe 6 (1976)
49. f(ωo,μ), Sem. Analyse Convexe 9 (1979) 17.1-17.7
50. C. CASTAING AND M. VALADIER, Convex analysis and measurable multifunctions, Lecture Notes in Math., vol. 580, SpringerVerlag Berlin, 1977
51. A. CELLINA AND G. COLOMBO, On classical problem of the calculus of variations without convexity assumptions, Ann. Inst. H. Poincare Analyse nonlineaire 7 (1989), 97-106
52. L. CESARI, Optimization-theory an applications, SpringerVerlag Berlin, 1983
53. S.D. CHATTERJI, A subsequence principle theory, Jber. d. Dt. Math. Verein 87 (1985), 91-107
54. G. CHOQUET, Lectures on analysis enjamin, Reading, Mass 1969
55. C. DELLACHERIE AND P.A. MEYER, Probability et potentiel, Hermann, Paris 1975, (English translation: North-Holland, Amsterdam, 1978)
56. J. DIESTEL AND J.J. UHL, Vector measures., Math. Surveys, vol 15 American Mathematical Society, Providence, RI, 1977
57. X.P. DING AND K.K. TAN, Generalized variational inequalities an generalized quasivariational inequalities, J. Math. Anal. Appl. 148 (1990), 497-508
58. I. EKELAND AND R. TEMAM, Convex analysis an variational problems, North-Holland, Amsterdam, 1977
59. KY. FAN, A generalization of Tychonoff's fixe point theorem, Math. Ann. 142 (1961), 305-310
60. T. FERGUSON, Mathematical statistics: a decision theoretic approach Academic Press, New York, 1967
61. F. GALDEANO AND A. TRUFFERT, On the narrow convergence of measures defined on a product space, Preprint, Departement de Mathematiques, Universite de Perpignan, 1999
62. J. GREENBERG, B. SHITOVITZ, AND A. WIECZOREK, Existence of equilibria in atomless production economies with price dependent preferences, J. Math. Econom. 6 (1979), 31-41
63. J.C. HARSANYI, Games with incomplete information playe by 'Bayesian' players, Management Sci. 14, pp. 159-182
64. T. ICHIISHI, Game theory for economic analysis, Academic Press, New York, 1983
65. A.D. IOFFE, On lower semicontinuity of integral functionals, i, ii SIAM J. Control Optim. 15 (1977), 521-538,991-1000
66. A. IONESCU TULCEA AND C, Topics in the theory of lifting Springer-Verlag, Berlin, 1969
67. J. JACOD AND J. MEMIN, Sur un type de convergence intermediaire entre la convergence en hi et la convergence en probability, Seminaire de Probabilites XV (J. Azema and M. Yor, eds.), Lecture Notes i Math., vol. 986, Springer-Verlag, Berlin, 1983, pp. 529-546
68. A. JAWHAR, Mesures de transition et applications, Sena. Analyse Con-vexe 14 (1984), 13.1-13.62
69. M.A. KHAN, On extensions of the Cournot-Nash theorem, Advances in Equilibrium Theory (CD. Aliprantis, O. Burkinshaw, and N.J Rothman, eds.), Lecture Notes Econ. Math. Syst, vol. 244, Springer Verlag, Berlin, 1985, pp. 79-106
70. M.A. KHAN AND A. RUSTICHINI, Cournot-Nash equilibrium distributions for games with differential information, Fixed Point Theory and Applications (M.A. Thera and J.B Baillon, eds), Pitman Research Notes, vol. 252, 1991, pp. 245-259
71. J. KOMLOS, A generalisation of a problem of Steinhaus, Acta Math. Acad. Sci. Hungar 18 (1967), 217-229
72. J. KRISTENSEN, Lower semicontinuity in spaces of weakly differen-tiable functions, Preprint, Mathematical Institute, University of Oxford, England
73. L. LECAM, An extension of Wald's theory of statistical ecision functions, Ann. Math. Stat. 26 (1955), 69-81
74. L. LECAM, Convergence in distribution of stochastic processes, Univ California Publ. Statist. 11 (1957), no. 2, 207-236
75. M. LOEVE, Probability theory i, SpringerVerlag erlin, 1977
76. C. MARICONDA, A generalization of the Cellina-Colombo theorem for a class of non-convex variational problems, J. Math. Anal. Appl. 175 (1993), 514-522
77. A. MAS-COLELL, On a theorem of Schmeiler, J. Math. Econom. 13 (1984), 201-206
78. P.R. MILGROM AND R.J. WEBER, Distributional strategies for games with incomplete information, Math. Oper. Res. 10 (1985), 619-632
79. B.S. MORDUCHOVICH, The existence of optimal controls in a problem with a free right terminal, Diff. Equations 8 (1972), 1545-1548
80. B.S. MORDUCHOVICH, Existence theorems in nonconvex optimal control, Proceedings of "Calculus of Variations and Related Topics" (Haifa), 1998, to appear
81. J. NEVEU, Mathematical foundations of the calculus of probability Holden-Day, San Fransisco, 1965
82. K.R. PARTHASARATHY, Probability measures on metric spaces, Aca-demic Press, New York, 1967
83. P. PEDREGAL, Parametrize measures an variational principles Birkhauser, Basel, 1997
84. J. PFANZAGL, Convexity an conditional expectations, Ann. Prob. 2 (1974), 490-494
85. K.P. RATH, Existence and upper hemicontinuity of equilibrium distributions of anonymous games with discontinuous payoffs, J. Math. Econom. 26 (1996), 305-324
86. J.P. RAYMOND, Existence theorems in optimal control theory without convexity assumptions, J. Optim. Theory Appl. 67 (1990), 109-132
87. D. SCHMEIDLER, Fatou's lemma in several dimensions, Proc. Amer Math. Soc. 24 (1970), 300-306
88. D. SCHMEIDLER, Equilibrium points of non-atomic games, J. Statist Phys. 7 (1973), 295-300
89. L. SCHWARTZ, Radon measures, University Press, Oxford, 1975
90. M. SYCHEV, Young measure approach to characterization of behaviour of integral functionals on weakly convergent sequences by means of their integrands, Ann. Inst. H. Poincare (Analyse Nonlineaire), to appear
91. L. TARTAR, Compensated compactness and aplications to partial differential equations, Nonlinear Analysis and Mechanics (R. Knops ed.), Res. Notes Math., vol. 39, Pitman, Boston, 1979, pp. 136-212
92. F. TOPSCE, Topology and measure, Lecture Notes in Math., vol. 133 Springer-Verlag, Berlin, 1970
93. M. VALADIER, Some bang-bang theorems, Multifunctions and Integrands (G. Salinetti, ed.), Lecture Notes in Math., vol 1091, Springer Verlag, Berlin, 1984, pp. 225-234
94. M. VALADIER, Young measures, Methods of Nonconvex Analysis (A. Cellina, ed.), Lecture Notes in Math., vol. 1446, SpringerVerlag Berlin, 1990, pp. 152-188
95. M. VALADIER, A course on Young measures, Rend. Istit. Mat. Univ Trieste 24 (1994), 349-394, supplemento
96. A. WALD, Statistical decision functions, Wiley, New York, 1950
97. J. WARGA, Optimal control of differential an functional equations Avademi Press, New York, 1972
98. L.C. YOUNG, Generalized curves and the existence of an attained absolute minimum in the calculus of variations, C. R. Sci. Lettres Varsovie 30 (1937), no. C III, 212-234