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The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.
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Stochastic partial differential equations are studied using the infinite dimensional stochastic analysis, the theory of evolution operators and rigged Hilbert spaces. The authors consider existence and uniqueness theorems as well as possibilities of the approximation.About the Author:
Wilfried Grecksch, Professor, Martin-Luther-University of Halle-Wittenberg, Faculty of Mathematics and Computer Science; Constantin Tudor, Professor, University of Bucharest, Faculty of Mathematics
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