Entropy minimization and schrodinger processes in infinite dimensions

Annals of Probability

Volumn 25, Issue 2, 1997, Pages 901-926

  Föllmer, Hans ^a   Gantert, Nina ^b  

^a HUMBOLDT UNIVERSITY   (Germany)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Brownian motion; Brownian sheet; Entropy minimization under given marginals; Large deviations; Relative entropy; Schr dinger processes; Space time harmonic functions; Stochastic mechanics

Indexed keywords

EID: 17544386282     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1024404423     Document Type: Article

References (22)

1. AEBI, R. (1996). Schrödinger Diffusion Processes. Birkhäuser, Basel.
2. BERNSTEIN, S. (1932). Sur les liaisons entre les grandeurs aléatoires. Verh. Internat. Math. Kongr. Zürich 1 288-309.
3. BEURLING, A. (1960). An automorphism of product measures. Ann. Math. 72 189-200.
4. BORWEIN, J. M. and LEWIS, A. S. (1992). Decomposition of multivariate functions. Canad. J. Math. 44 463-482.
5. BORWEIN, J. M., LEWIS, A. S. and NUSSBAUM, R. (1994). Entropy minimization, DAD problems, and doubly stochastic kernels. J. Funct. Anal. 123 264-307.
6. BROCKHAUS, O. (1995). Konditionierungen des Brownschen Blattes: Große Abweichungen und Schrödinger-Brücken. Bonner Math. Schriften 285.
7. CSISZÁR, I. (1975). I-divergence geometry of probability distribution and minimization problems. Ann. Probab. 3 146-158.
8. DAWSON, D., GOROSTIZA, L. and WAKOLBINGER, A. (1990). Schrödinger processes and large devia-tions. J. Math. Phys. 31 2385-2388.
9. DONSKER, M. D. and VARADHAN, S. R. S. (1975). Asymptotic evaluation of certain Markov process expectations for large time. III. Comm. Pure Appl. Math. 29 389-461.
10. DOOB, J. L. (1984). Classical Potential Theory and Its Probabilistic Counterpart. Springer, New York.
11. FÖLLMER, H. (1988). Random fields and diffusion processes. Ecole d'Eté de Saint Flour XV-XVII. Lecture Notes in Math. 1362 101-203. Springer, New York.
12. FÖLLMER, H. (1991). Martin boundaries on Wiener Space. In Diffusions Processes and Related Problems in Analysis. I (M. Pinsky, ed.). 3-16. Birkhäuser, Basel.
13. FORTET, R. (1940). Résolution d'un systeme d'équations de M. Schrödinger. J. Math. Pures Appl. (9) 83-105.
14. GANTERT, N. (1994). Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree. Probab. Theory Related Fields 98 7-20.
15. JAMISON, B. (1974). Reciprocal processes. Z. Wahrsch. Verw. Gebiete 30 65-86.
16. JAMISON, B. (1975). The Markov process of Schrödinger. Z. Wahrsch. Verw. Gebiete 32 323-331.
17. NAGASAWA, M. (1993). Schrödinger Equations and Diffusion Theory. Birkhäuser, Basel.
18. RÜSCHENDORF, L. and THOMSEN, W. (1993). Note on the Schrödinger equation and I-projections. Statist. Probab. Lett. 17 369-375.
19. SCHRÖDINGER, E. (1931). Über die Umkehrung der Naturgesetze. Sitzungsber. Preuss. Akad. Wiss. Berlin Phys. Math. Kl. 8/9 144-153.
20. SCHRÖDINGER, E. (1932). Sur la théorie relativiste de l'électron et l'interprétation de la mécanique quantique. Ann. Inst. H. Poincaré 2 269-310.
21. THIEULLEN, M. (1993). Second order stochastic differential equations and non gaussian reciprocal diffusions. Probab. Theory Related Fields 97 231-257.
22. THIEULLEN, M. and ZAMBRINI, J. C. (1995). Symmetries in stochastic calculus of variations. Preprint, Laboratoire de Probabilités, Univ. Paris VI.