Lyapunov exponents for stochastic Anderson models with non-gaussian noise

Stochastics and Dynamics

Volumn 8, Issue 3, 2008, Pages 451-473

  Kim, Ha Young ^a   Viens, Frederi G ^a   Vizcarra, Andrew B ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

Anderson model; Feynman Kac formula; Lyapunov exponent; Malliavin derivative; Non Gaussian; Polymer; Random environment; Strong disorder

Indexed keywords

EID: 56549109742     PISSN: 02194937     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219493708002408     Document Type: Conference Paper

References (21)

1. R. Adler, An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes (Inst. Math. Stat., 1990).
2. L. Arnold, Random Dynamical Systems (Springer-Verlag, 1998).
3. B. Berge, I. D. Chueshov and P.-A. Vuillermot, Lyapunov exponents and stability for nonlinear SPDE's driven by finite-dimensional Wiener processes, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 215-220.
4. L. Bertim and G. Giacomin, On the long-time behavior of the stochastic heat equation, Probab. Th. Relat. Fields 114 (1999) 279-289.
5. A. Cadel, S. Tindel and F. Viens, Sharp asymptotics for the partition function of some continuous-time directed polymers, preprint, 30 pages, Available at http://arxiv.org/PS_cashe/arxiv/pdf/0710/0710.0942v1.pdf.
6. R. A. Carmona, L. Koralov and S. A. Molchanov, Asymptotics for the almost sure Lyapunov exponent for the solution of the parabolic Anderson problem, Random Oper. Stoch. Eqns. 9 (2001) 77-86.
7. R. A. Carmona and S. A. Molchanov, Parabolic Anderson Model and Intermittency, Memoirs A.M.S., Vol. 418 (Amer. Math. Soc., 1994).
8. R. A. Carmona, S. A. Molchanov and F. Viens, Sharp upper bound on exponential behavior of a stochastic partial differential equation, Random Oper. Stoch. Eqns. 4 (1996) 43-49.
9. R. A. Carmona and F. Viens, Almost-sure exponential behavior of a stochastic Anderson model with continuous space parameter, Stoch. Stoch. Rep. 62 (1998) 251-273.
10. F. Comets and V. Vargas, Majorizing multiplicative cascades for directed polymers in random media. ALEA Lat. Amer. J. Probab. Math. Stat. 2 (2006) 267-277 (electronic).
11. M. Cranston, T. Mountford and T. Shiga, Lyapunov exponents for the parabolic Anderson model, Acta Math. Univ. Comenianae LXXI (2002) 163-188.
12. I. Florescu and F. Viens, Sharp estimation for the almost-sure Lyapunov exponent of the Anderson model in continuous space, Probab. Th. Relat. Fields 135 (2006) 603-644.
13. J. Gartner, W. Konig and S. A. Molchanov, Almost sure asymptotics for the continuous parabolic Anderson model, Probab. Th. Relat.Fields 118 (2000) 547-573.
14. M. Ledoux and M. Talagrand, Probability in Banach Spaces (Springer-Verlag, 1991).
15. S. Molchanov and A. Ruzmaikin, Lyapunov exponents and distributions of magnetic fields in dynamo models, Progr. Probab. 34 (1994) 287-306.
16. D. Nualart, The Malliavin Calculus and Related Topics, 2nd edn. (Springer-Verlag, 2006).
17. V. I. Oseledets, A multiplicative ergodic theorem, Characteristic Lyapunov, exponents of dynamical systems (Russian), Trudy Moskov. Mat. Obšč. 19 (1968) 179-210.
18. C. Rovira and S. Tindel, On the Brownian directed polymer in a Gaussian random environment, J. Funct. Anal. 222 (2005) 178-201.
19. S. Tindel and F. Viens, Almost sure exponential behaviour for a parabolic SPDE on a manifold, Stoch. Process. Appl. 100 (2002) 53-74.
20. S. Tindel and F. Viens, Relating the almost-sure Lyapunov exponent of a parabolic SPDE and its coefficients' spatial regularity, Potential Anal. 22 (2005) 101-125.
21. A.-S. Üstünel, An Introduction to Analysis on Wiener Space, Lecture Notes in Mathematics, Vol. 1610 (Springer-Verlag, 1995).