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


93E15 Stochastic stability in control theory
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
93C25 Control/observation systems in abstract spaces
93C10 Nonlinear systems in control theory
60H05 Stochastic integrals
60G17 Sample path properties
Full Text: DOI


[1] Arnold, L., Stochastic Differential Equations: Theory and Applications (1974), Wiley: Wiley New York · Zbl 0278.60039
[2] Balakrishnan, A. V., Applied Functional Analysis (1976), Springer-Verlag: Springer-Verlag New York · Zbl 0333.93051
[3] Chojnowska-Michalik, A., Stochastic Differential Equations in Hilbert Spaces and Their Applications, (Thesis (1976), Institute of Mathematics, Polish Academy of Sciences) · Zbl 0547.60067
[4] Curtain, R. F.; Falb, P. L., Ito’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), Springer-Verlag: Springer-Verlag New York/Berlin) · 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, Vol. 4 (1964), Academic Press: Academic Press New York) · Zbl 0136.11201
[9] Gikhman, I. I.; Skorokhod, A. V., Introduction to the Theory of Random Processes (1969), Saunders: Saunders Philadelphia · Zbl 0429.60002
[10] Gihman, I. I.; Skorohod, A. V., Stochastic Differential Equations (1972), Springer-Verlag: Springer-Verlag New York/Berlin · 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, Vol. 31 (1957), American Mathematical Society, Colloquium Publication: American Mathematical Society, Colloquium Publication Providence, R. I) · 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) · Zbl 0325.60054
[16] Pardoux, E., Equations aux Dérivées Partielles Stochastiques Nonlinéaires Monotones, (Thesis (1975), L’université Paris Sud) · Zbl 0576.60049
[17] Pardoux, E., Intégrales Stochastiques Hilbertiennes, (Cahier de Mathématiques de la Décision (1976), Université Paris-Dauphiné)
[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, (Ciesielski, Z., Probability Theory, Vol. 5 (1979), Banach Center Publications: Banach Center Publications Warsaw), 273-281 · Zbl 0435.93047
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