Bo, Lijun; Jiang, Yiming; Wang, Yongjin On a class of stochastic Anderson models with fractional noises. (English) Zbl 1136.60345 Stochastic Anal. Appl. 26, No. 2, 256-273 (2008). Summary: We are concerned with a class of one-dimensional fourth order stochastic Anderson models with double-parameter fractional noises with Hurst parameter \(H = (h_1, h_2)\in (\frac 1 2 , 1)\times (\frac 1 2 , 1)\). The unique solution is constructed for the model in some appropriate Hilbert space. On the other hand, we shall estimate the Lyapunov exponent of the solution and study its regularity. Cited in 19 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 34A34 Nonlinear ordinary differential equations and systems, general theory 49N60 Regularity of solutions in optimal control Keywords:fourth order Anderson models; fractional noises; Lyapunov exponent; regularity PDF BibTeX XML Cite \textit{L. Bo} et al., Stochastic Anal. Appl. 26, No. 2, 256--273 (2008; Zbl 1136.60345) Full Text: DOI References: [1] DOI: 10.1142/S0219493706001736 · Zbl 1098.60058 · doi:10.1142/S0219493706001736 [2] DOI: 10.2307/3318542 · Zbl 0995.60058 · doi:10.2307/3318542 [3] DOI: 10.1007/s004400050248 · Zbl 0952.60043 · doi:10.1007/s004400050248 [4] Eidelman S.D., Parabolic Boundary Value Problems (1998) [5] DOI: 10.1007/s00245-001-0001-2 · Zbl 0993.60065 · doi:10.1007/s00245-001-0001-2 [6] DOI: 10.1023/A:1024878703232 · Zbl 0993.60063 · doi:10.1023/A:1024878703232 [7] DOI: 10.1016/S0167-7152(00)00157-7 · Zbl 0983.60052 · doi:10.1016/S0167-7152(00)00157-7 [8] DOI: 10.1007/BF01192141 · Zbl 0729.60055 · doi:10.1007/BF01192141 [9] Mueller C., Progress in Probabilty 52 pp 219– (2002) [10] DOI: 10.1142/S0219493704001012 · Zbl 1080.60065 · doi:10.1142/S0219493704001012 [11] DOI: 10.1006/jfan.1996.3091 · Zbl 0894.60054 · doi:10.1006/jfan.1996.3091 [12] DOI: 10.1016/0022-1236(89)90098-0 · Zbl 0682.60046 · doi:10.1016/0022-1236(89)90098-0 [13] Podlubny I., Fractional Differential Equations (1999) · Zbl 0924.34008 [14] DOI: 10.1080/07362999608809452 · Zbl 0876.60043 · doi:10.1080/07362999608809452 [15] Walsh J., An Introduction to Stochastic Partial Differential Equations. Lecture Notes in Math (1986) · Zbl 0608.60060 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.