Relating the almost-sure lyapunov exponent of a parabolic SPDE and its coefficients' spatial regularity

Potential Analysis

Volumn 22, Issue 2, 2005, Pages 101-125

  Tindel, Samy ^a   Viens, Frederi ^b  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^b PURDUE UNIVERSITY   (United States)

Author keywords

Feynman Kac formula; Gaussian regularity; Lyapunov exponent; Parabolic stochastic partial differential equations

Indexed keywords

EID: 15444361840     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11118-004-0576-8     Document Type: Article

References (14)

1. Adler, R.: An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes, Inst. Math. Stat., Hayward, CA, 1990.
2. Berge, B., Chueshov, I.D. and Vuillermot, P.-A.: 'Lyapunov exponents and stability for nonlinear SPDE's driven by finite-dimensional Wiener processes', C.R. Acad. Sci. Paris Sér. I Math. 329(3) (1999), 215-220.
3. Bertini, L. and Giacomin, G.: 'On the long-time behavior of the stochastic heat equation', Probab. Theory Related Fields 114(3) (1999), 279-289.
4. Carmona, R.A. and Molchanov, S.A.: Parabolic Anderson Model and Intermittency, Mem. Amer. Math. Soc. 418, 1994.
5. Carmona, R.A., Molchanov, S.A. and Viens, F.G.: 'Sharp upper bound on exponential behavior of a stochastic partial differential equation', Random Operators and Stochastic Equations 4(1) (1996), 43-49.
6. Carmona, R. and Viens, F.: 'Almost-sure exponential behavior of a stochastic Anderson model with continuous space parameter', Stochastics Stochastics Rep. 62(3-4) (1998), 251-273.
7. Cranston, M., Mountford, T.S. and Shiga, T.: 'Lyapunov exponents for the parabolic Anderson model', Acta Math. Univ. Comenian. (N.S.) 71(2) (2002), 163-188.
8. Da Prato, G. and Zabczyk, J.: Stochastic Equations in Infinite Dimensions, Cambridge Univ. Press, 1992.
9. Dalang, R. and Frangos, N.: 'The stochastic wave equation in two spatial dimensions', Ann. Probab. 26 (1998), 187-212.
10. Gartner, J., Konig, W. and Molchanov, S.A.: 'Almost sure asymptotics for the continuous parabolic Anderson model', Probab. Theory Related Fields 118(4) (2000), 547-573.
11. Karatzas, I. and Shreve, S.: Brownian Motion and Stochastic Calculus, 2nd edn, Springer, 1991.
12. Millet, A. and Sanz-Sole, M.: 'A stochastic wave equation in two spatial dimensions: Smoothness of the law', Ann. Probab. 27(2) (1999), 803-844.
13. Peszat, S. and Zabczyk, J.: 'Nonlinear stochastic wave and heat equations', Probab. Theory Related Fields 116(3) (2000), 421-443.
14. Tindel, S. and Viens, F.: 'Almost sure exponential behaviour for a parabolic SPDE on a manifold', Stochastic Process. Appl. 100 (2002), 53-74.