Action minimizing stochastic invariant measures for a class of Lagrangian systems

Communications on Pure and Applied Analysis

Volumn 7, Issue 5, 2008, Pages 1211-1223

  Wang, Kaizhi ^a  

^a JILIN UNIVERSITY   (China)

Author keywords

Action minimizing stochastic invariant measures; Lagrangian systems; Stochastic mather's functions; Variational method

Indexed keywords

EID: 48249154240     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2008.7.1211     Document Type: Article

References (10)

1. G. Aronsson, Minimization problems for the functional supF(x, f(x), f′(x)), Ark. Mat., 6 (1965), 33-53.
2. L. Evans, Some new PDE methods for weak KAM theory, Calc. Var., 17 (2003), 159-177.
3. L. Evans and D. Gomes, Effective Hamiltonians and averaging for Hamiltonian dynamics I, Arch. Ration. Mech. Anal., 157 (2001), 1-33.
4. W. Fleming and H. Soner, "Controlled Markov Processes and Viscosity Solutions," Springer-Verlag, New York, 1993.
5. D. Gomes, A stochastic analogue of Aubry-Mather theory, Nonlinearity, 15 (2002), 581-603.
6. N. Krylov, "Nonlinear Elliptic and Parabolic Equations of the Second Order," D. Reidel Publishing Co., Dordrecht, 1987. Translated from the Russian by P.L. Buzytsky.
7. J. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z., 207 (1991), 169-207.
8. E. Nelson, "Quantum Fluctuations," Pricetin Univ. Press, Priceton, NJ, 1985.
9. T. Rockafellar, "Convex Analysis," Princeton University Press, 1972.
10. R. Iturriaga and H. Morgado, On the stochastic Aubry-Mather theory, Bol. Soc. Mat. Mexicana 11 (2005), 91-99.