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Stability of semilinear stochastic evolution equations. (English) Zbl 0497.93055

93E15Stochastic stability
60H15Stochastic partial differential equations
35G10Initial value problems for linear higher-order PDE
35K25Higher order parabolic equations, general
93C25Control systems in abstract spaces
93C10Nonlinear control systems
60H05Stochastic integrals
60G17Sample path properties
Full Text: DOI
[1] Arnold, L.: Stochastic differential equations: theory and applications. (1974) · Zbl 0278.60039
[2] Balakrishnan, A. V.: Applied functional analysis. (1976) · Zbl 0333.93051
[3] Chojnowska-Michalik, A.: Stochastic differential equations in Hilbert spaces and their applications. Thesis (1976) · Zbl 0414.60064
[4] Curtain, R. F.; Falb, P. L.: Itô’s lemma in infinite dimensions. J. math. Anal. appl. 31, 434-448 (1970) · Zbl 0233.60051
[5] Curtain, R. F.; Falb, P. L.: Stochastic differential equations in Hilbert spaces. J. diferential equations 10, 412-430 (1971) · Zbl 0225.60028
[6] Curtain, R. F.; Pritchard, A. J.: Infinite dimensional linear system theory. Lecture notes in control and information sciences no. 8 (1978) · Zbl 0426.93001
[7] Curtain, R. F.: Stability of stochastic partial differential equation. J. math. Anal. appl. 79, 352-369 (1981) · Zbl 0452.60072
[8] Gel’fand, I. M.; Vilenkin, N. Ya: Generalized functions. 4 (1964)
[9] Gikhman, I. I.; Skorokhod, A. V.: Introduction to the theory of random processes. (1969) · Zbl 0132.37902
[10] Gihman, I. I.; Skorohod, A. V.: Stochastic differential equations. (1972) · Zbl 0242.60003
[11] Haussmann, U. G.: Asymptotic stability of the linear ito’equation in infinite dimensions. J. math. Anal. appl. 65, 219-235 (1978) · Zbl 0385.93051
[12] Hille, E.; Phillips, R. S.: Functional analysis and semigroups. 31 (1957) · Zbl 0078.10004
[13] Ichikawa, A.: Linear stochastic evolution equations in Hilbert space. J. differential equations 28, 266-277 (1978) · Zbl 0348.60087
[14] Ichikawa, A.: Dynamic programming approach to stochastic evolution equations. SIAM J. Control optim. 17, 152-174 (1979) · Zbl 0434.93069
[15] Métivier, M.; Pistone, G.: Une formula d’isométrie pour l’intègrale stochatique et équations d’évolution linéares stochastiques. Z. warsch. Verw. gebiete 33, 1-18 (1975)
[16] Pardoux, E.: Equations aux dérivées partielles stochastiques nonlinéaires monotones. Thesis (1975)
[17] Pardoux, E.: Intégrales stochastiques hilbertiennes. Cahier de mathématiques de la décision (1976)
[18] Scalora, F. S.: Abstract martingale convergence theorems. Pacific J. Math. 11, 347-374 (1961) · Zbl 0114.07702
[19] Zabczyk, J.: On stability of infinite dimensional stochastic systems. Probability theory 5, 273-281 (1979) · Zbl 0435.93047