Minimizers of energy functionals

Acta Mathematica Hungarica

Volumn 93, Issue 4, 2001, Pages 281-325

  Leonard C ^a,b  

^a Modal X   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Convex conjugacy; Convex integral functionals; Marginal problems; Maximum entropy method; Orlicz spaces

Indexed keywords

EID: 23544453246     PISSN: 02365294     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (37)

1. A. Beurling, An automorphism of product measures, Ann. Math., 72 (1960), 189-200.
2. J. M. Borwein and A. S. Lewis, Duality relationships for entropy-like minimization problems, SIAM J. Control and Optim., 29 (1991), 325-338.
3. J. M. Borwein and A. S. Lewis, On the convergence of moment problems, Trans. Amer. Math. Soc., 325 (1991), 249-271.
4. J. M. Borwein and A. S. Lewis, Convergence of best entropy estimates, SIAM J. Optim., 1 (1991), 191-205.
5. 1 and the existence of maximum entropy estimates, SIAM J. Optim., 3 (1993), 248-267.
6. J. M. Borwein and A. S. Lewis, Strong rotundity and optimization, SIAM J. Optim., 4 (1994), 146-158.
7. J. M. Borwein and A. S. Lewis, Decomposition of multivariate functions, Can. J. Math., 44 (1992), 463-482.
8. J. M. Borwein, A. S. Lewis and R. D. Nussbaum, Entropy minimization, DAD problems and doubly stochastic kernels, J. Funct. Anal., 123 (1994), 264-307.
9. J. M. Borwein, On the failure of maximum entropy reconstruction for Fredholm equations and other infinite systems, Math. Programming, 61 (1993), 251-261.
10. N. Bourbaki, Espaces vectoriels topologiques, Masson (Paris, 1981).
11. P. Cattiaux and H. Föllmer, Private communication.
12. P. Cattiaux and C. Léonard, Large deviations and Nelson processes, Forum Math., 7 (1995), 95-115.
13. P. Cattiaux and F. Gamboa, Large deviations and variational theorems for marginal problems, Bernoulli, 5 (1999).
14. I. Csiszár, F. Gamboa and E. Gassiat, MEM pixel correlated solutions for generalized moment and interpolation problems, IEEE Trans. Inform. Theory., 45 (1999), 2253-2270.
15. I. Csiszár, I-divergence geometry of probability distributions and minimization problems, Ann. Probab., 3 (1975), 146-158.
16. I. Csiszár, Sanov property, generalized I-projection and a conditional limit theorem, Ann. Probab., 12 (1984), 768-793.
17. I. Csiszár, Generalized projections for non-negative functions, Acta Math. Hungar., 68 (1995), 161-185.
18. A. B. Cruzeiro, Liming Wu and J. C. Zambrini, Bernstein processes associated with a Markov process, in: Proceedings of the Third International Workshop on Stochastic Analysis and Mathematical Physics: ANESTOC'98, Ed. R. Rebolledo, Trends in Mathematics, Birkhaüser.
19. D. A. Dawson and J. Gärtner, Large deviations from the McKean-Vlasov limit for weakly interacting diffusions, Stochastics and Stoch. Rep., 20 (1987), 247-308.
20. D. Dacunha-Castelle and F. Gamboa, Maximum d'entropie et problèmes de moments, Ann. Inst. Henri Poincaré, 26 (1990), 567-596.
21. P. Dai Pra, A stochastic control approach to reciprocal diffusion processes, Appl. Math. Optim., 23 (1991), 313-329.
22. I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland (Amsterdam, 1976).
23. H. Föllmer and N. Gantert, On Schrödinger processes in infinite dimensions, Ann. Probab., 25 (1997), 901-926.
24. H. Föllmer, Random Fields and Diffusion Processes, Cours à l'Ecole d'Été de Probabilités de Saint-Flour (1988), Lecture Notes in Mathematics 1362, Springer-Verlag.
25. F. Gamboa and E. Gassiat, Bayesian methods and maximum entropy for ill posed problems, Ann. Statist., 25 (1997), 328-350.
26. A. Kozek, Convex integral functionals on Orlicz spaces, Ann. Soc. Math. Polonae, Series I (1979), 109-135.
27. C. Léonard, Convex conjugates of integral functionals, Acta Math. Hungar., 93 (2001), 253-280.
28. C. Léonard, Minimization of energy functionals applied to some inverse problems, to appear in J. Appl. Math. Optim.
29. F. Liese and I. Vajda, Convex Statistical Distances, B. G. Teubner (Leipzig, 1987).
30. D. Pollard, Convergence of Stochastic Processes, Springer Verlag (1984).
31. M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker Inc. (New York, 1991).
32. R. T. Rockafellar, Conjugate Duality and Optimization, SIAM (Philadelphia, 1974).
33. W. Rudin, Analyse Fonctionnelle, Ediscience international (Paris, 1995).
34. L. Rüschendorf, On the minimum discrimination information theorem, Statist. Decisions, Supplementary volume 1 (1984).
35. L. Rüschendorf and W. Thomsen, Note on the Schrödinger equation and I-projections. Statistics Probability Letters, 17 (1993), 369-375.
36. M. Teboulle and I. Vajda, Convergence of best φ-entropy estimates, IEEE Trans. Inform. Theory, 39 (1993), 297-301.
37. J. C. Zambrini, Variational processes and stochastic versions of mechanics, J. Math. Phys., 27 (1986), 2307.