Previous |  Up |  Next

Article

Keywords:
stochastic evolution equations; integral continuity theorems; asymptotic stability; stochastic partial differential equations; semigroup approach
Summary:
In the present paper integral continuity theorems for solutions of stochastic evolution equations of parabolic type on unbounded time intervals are established. For this purpose, the asymptotic stability of stochastic partial differential equations is investigated, the results obtained being of independent interest. Stochastic evolution equations are treated as equations in Hilbert spaces within the framework of the semigroup approach.
References:
[1] A. V. Balakrishnan: Applied functional analysis. Springer-Verlag, New York-Heidelberg- Berlin 1976. MR 0470699 | Zbl 0333.93051
[2] P. L. Butzer H. Berens: Semi-groups of operators and approximation. Springer-Verlag, Berlin-Heidelberg-New York 1967. MR 0230022
[3] N. Dunford J. T. Schwartz: Linear operators, Part II. Interscience, New York-London 1963. MR 0188745
[4] A. H. Филатов: Методы усреднения в дифференциальных и интегродифференциальных уравнениях. Фан, Tашкент 1971. Zbl 1168.35423
[5] A. Friedman: Stochastic differential equations and applications. vol. 1. Academic Press, New York 1975. MR 0494490 | Zbl 0323.60056
[6] T. Funaki: Random motion of strings and related stochastic evolution equations. Nagoya Math. J. 89 (1983), 129-193. MR 0692348 | Zbl 0531.60095
[7] A. Ichikawa: Stability of semilinear stochastic evolution equations. J. Math. Anal. Appl. 90 (1982), 12-44. DOI 10.1016/0022-247X(82)90041-5 | MR 0680861 | Zbl 0497.93055
[8] A. Ichikawa: Semilinear stochastic evolution equations: boundedness, stability and invariant measures. Stochastics 12 (1984), 1 - 39. DOI 10.1080/17442508408833293 | MR 0738933 | Zbl 0538.60068
[9] B. Maslowski: On some stability properties of stochastic differential equations of Itó's type. Časopis pěst. mat. 111 (1986), 404-423. MR 0871716 | Zbl 0625.60066
[10] J. Seidler I. Vrkoč: An averaging principle for stochastic evolution equations. Časopis pěst. mat. 115 (1990), 240-263. MR 1071056
[11] I. Vrkoč: Extension of the averaging method to stochastic equations. Czechoslovak Math. J. 16 (91) (1966), 518-544. MR 0205318
Partner of
EuDML logo