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Stability of mild solutions of stochastic evolution equations with variable delay. (English) Zbl 1036.60052
Semilinear stochastic evolution equations with delays are considered. Existence and stability results for mild solutions are obtained.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[1] Arnold L., Report No. 17, in: Nonlinear Stochastic Evolution Equation in Hilbert Space (1980)
[2] DOI: 10.1016/0022-247X(82)90110-X · Zbl 0496.60059 · doi:10.1016/0022-247X(82)90110-X
[3] Govindan T. E., Comm. Appl. Anal. 7 pp 102– (2003)
[4] Ichikawa A., Stochastics 12 pp 1– (1984) · Zbl 0538.60068 · doi:10.1080/17442508408833293
[5] DOI: 10.1006/jmaa.1997.5534 · Zbl 0885.60044 · doi:10.1006/jmaa.1997.5534
[6] Mao X., Exponential Stability of Stochastic Differential Equations (1994) · Zbl 0806.60044
[7] DOI: 10.1080/07362999908809633 · Zbl 0943.60050 · doi:10.1080/07362999908809633
[8] Liu K., Stochastics and Stochastics Reports 63 pp 1– (1998) · Zbl 0947.93037 · doi:10.1080/17442509808834140
[9] DOI: 10.1093/qmath/42.1.77 · Zbl 0719.60062 · doi:10.1093/qmath/42.1.77
[10] DOI: 10.1080/07362999808809573 · Zbl 0911.60054 · doi:10.1080/07362999808809573
[11] Kolmanovskii V. B., Stability of Functional Differential Equations (1986)
[12] DOI: 10.1081/SAP-120015832 · Zbl 1066.60055 · doi:10.1081/SAP-120015832
[13] DOI: 10.1080/07362999908809612 · Zbl 0940.60076 · doi:10.1080/07362999908809612
[14] DOI: 10.1017/CBO9780511666223 · doi:10.1017/CBO9780511666223
[15] Ladde G. S., Random Differential Inequalities (1980) · Zbl 0466.60002
[16] DOI: 10.1016/0022-0396(92)90148-G · Zbl 0744.34052 · doi:10.1016/0022-0396(92)90148-G
[17] Laksmikantham V., Differential and Integral Inequalities: Theory and Applications (1969) · Zbl 0142.06406
[18] DOI: 10.1006/jmaa.1996.0179 · Zbl 0851.34077 · doi:10.1006/jmaa.1996.0179
[19] Rodkina A. E., Stochastics 12 pp 187– (1984) · Zbl 0568.60062 · doi:10.1080/17442508408833300
[20] Yamada T., J. Math. Kyoto Univ. 21 pp 501– (1981)
[21] Chukwu E. N., Stability and Time-Optimal Control of Hereditary Systems (1992) · Zbl 0751.93067
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