Bates, Peter W.; Lisei, Hannelore; Lu, Kening Attractors for stochastic lattice dynamical systems. (English) Zbl 1105.60041 Stoch. Dyn. 6, No. 1, 1-21 (2006). For dynamical systems described by infinite-dimensional stochastic differential equations (SDEs) on a one-dimensional lattice, stability and existence of random attractors are established. The class of SDE systems under consideration is characterised by independent additive Wiener processes in each component, dissipation terms, nonlinearity which also helps dissipation, and diffusive type interaction between neighbour particles via discrete Laplace operator. For such SDE systems, existence, uniqueness, continuous dependence on initial data, and a priori bounds for solutions have been proved. Existence of a unique compact global random attractor in the class of tempered sets is established. Reviewer: Alexander Yu. Veretennikov (Leeds) Cited in 224 Documents MSC: 60H15 Stochastic partial differential equations (aspects of stochastic analysis) Keywords:stochastic lattice differential equations; random attractors PDFBibTeX XMLCite \textit{P. W. Bates} et al., Stoch. Dyn. 6, No. 1, 1--21 (2006; Zbl 1105.60041) Full Text: DOI References: [1] DOI: 10.1142/S0218127494000459 · Zbl 0870.58049 [2] DOI: 10.1007/978-3-662-12878-7 [3] DOI: 10.1007/BF01192196 · Zbl 0821.60061 [4] DOI: 10.1007/s002050050189 · Zbl 0956.74037 [5] DOI: 10.1142/S0218127401002031 · Zbl 1091.37515 [6] DOI: 10.1016/0025-5564(81)90085-7 · Zbl 0454.92009 [7] Bell J., Quart. Appl. Math. 42 pp 1– · Zbl 0536.34050 [8] DOI: 10.1109/81.473583 [9] DOI: 10.1006/jdeq.1998.3478 · Zbl 0911.34050 [10] Chow S.-N., Random Comput. Dyn. 4 pp 109– [11] DOI: 10.1137/S0036139994261757 · Zbl 0840.34012 [12] DOI: 10.1109/81.222795 · Zbl 0800.92041 [13] DOI: 10.1109/31.7600 · Zbl 0663.94022 [14] DOI: 10.1109/31.7601 [15] DOI: 10.1109/81.251828 · Zbl 0844.93056 [16] DOI: 10.1017/S0024610700001915 · Zbl 1011.37032 [17] DOI: 10.1007/BF02219225 · Zbl 0884.58064 [18] DOI: 10.1007/BF01193705 · Zbl 0819.58023 [19] DOI: 10.1142/S0218127498000152 · Zbl 0933.37042 [20] DOI: 10.1017/CBO9780511666223 [21] DOI: 10.1016/0167-2789(93)90208-I · Zbl 0787.92010 [22] DOI: 10.1081/SAP-200029481 · Zbl 1063.60089 [23] DOI: 10.1080/17442509608834083 · Zbl 0870.60057 [24] DOI: 10.1023/A:1016673307045 · Zbl 1004.37034 [25] Kapval R., J. Math. Chem. 6 pp 113– [26] DOI: 10.1007/978-1-4612-0949-2 [27] DOI: 10.1137/0147038 · Zbl 0649.34019 [28] DOI: 10.1016/S0022-5193(05)80465-5 [29] Kunita H., Stochastic Flows and Stochastic Differential Equations (1997) · Zbl 0865.60043 [30] DOI: 10.1021/j100191a038 [31] DOI: 10.1109/81.473584 [32] DOI: 10.1023/A:1021841618074 · Zbl 0921.34046 [33] DOI: 10.1007/978-3-662-02847-6 [34] DOI: 10.1007/978-1-4612-5561-1 · Zbl 0516.47023 [35] Rashevsky N., Mathematical Biophysics 1 (1960) · JFM 64.1148.01 [36] DOI: 10.1007/BF01258529 · Zbl 0565.76031 [37] DOI: 10.1007/s00013-002-8241-1 · Zbl 1100.37032 [38] DOI: 10.1007/BF02479046 [39] DOI: 10.1137/S0036139995282670 · Zbl 0868.58059 [40] DOI: 10.1007/978-1-4612-4838-5 [41] DOI: 10.1016/0022-0396(92)90142-A · Zbl 0752.34007 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.