Symmetries in the stochastic calculus of variations

Probability Theory and Related Fields

Volumn 107, Issue 3, 1997, Pages 401-427

  Thieullen, M ^a   Zambrini, J C ^b  

^a University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^b UNIVERSITY OF LISBON   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031512583     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004400050091     Document Type: Article

References (19)

1. Arnold, V.: Méthodes mathématiques de la mécanique classique. Moscow: Editions Mir, 1976
2. Beurling, A.: An automorphism of product measures. Ann. Math. 72, No. 1, 189-200 (1960)
3. Bluman, G.W., Kumei, S.: Symmetries and differential equations. Applied Mathematical Sciences, 81, Berlin Heidelberg New York: Springer
4. Cattiaux, P., Léonard, C : Minimization of the Kullback information of diffusion processes, Ann. Inst. Henri Poincaré 30, No. 1, 83-132 (1994)
5. Dai Pra, P.: A stochastic control approach to reciprocal diffusion processes. Appl. Math. Opt. 23, 313-329 (1991)
6. Fleming, W.H., Soner, H.M.: Controlled Markov processes and viscosity solutions. Berlin: Springer 1993
7. Föllmer, H.: Random fields and diffusion processes. Ecole d'Eté de Probabilités de Saint Flour XV-XVIII, 1985-1987 (Lect. Notes Math., Vol. 1362) Berlin: Springer
8. Föllmer, H.: Time reversal on Wiener space. Proc. Bielefeld, 1984, 119-129. (Lect. Notes Math. Vol. 1158) Berlin: Springer
9. Hida, T.: Brownian motion. Berlin: Springer 1980
10. Ikeda, N., Watanabe, S.: Stochastic Differential equations and diffusion processes. Kodansha: North-Holland, 1981
11. Jamison, B.: Reciprocal processes. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 30, 65-86 (1974)
12. Krener, A.J.: Reciprocal diffusion and stochastic differential equations of second order. Stochastics 24, 393-422 (1988)
13. Logan, J.D.: Invariant variational principles. New York: Academic Press 1977
14. Nelson, E.: Dynamical theories of brownian motion. Princeton: Princeton Univ. Press 1967
15. Schrödinger, E.: Sur la théorie relativiste de l' électron et l' interprétation de la mécanique quantique. Ann. Inst. Henri Poincaré 2, 269-3 0 (1932)
16. Thieullen, M.: Second order stochastic differential equations and non gaussian reciprocal diffusions. Probab. Theory. Relat. Fields 97, 231-257 (1993)
17. Thieullen, M., Zambrini, J.C.: Probability and Quantum Symmetries. 1. The Theorem of Noether in Schrödinger's Euclidean Quantum Mechanics. Ann. Inst. Henri Poincaré (to appear)
18. Wakolbinger, A.: A simplified variational characterization of Schrödinger processes. J. Math. Phys. 30, 2943-2946 (1989)
19. Zambrini, J.C.: Variational processes and stochastic versions of mechanics. J. Math. Phys. 27, 2307-2330 (1986)