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Foundations of stochastic differential equations in infinite dimensional spaces. (English) Zbl 0547.60064
CBMS-NSF Regional Conference Series in Applied Mathematics 47. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (ISBN 0-89871-193-2). ix, 70 p. (1984).
This is a self-contained monograph on stochastic differential equations on Schwartz distribution spaces. Chapter 1 covers the background on distribution theory and in chapter 2 infinite-dimensional random variables and distributional stochastic processes are discussed. In the last chapter stochastic differential equations on distribution spaces are treated; in particular, various Ornstein-Uhlenbeck equations, which have been treated elsewhere in the literature from a different point of view.
Other more general theories for stochastic evolution equations may be found in M. Métivier and J. Pellaumail [Stochastic Integration. New York etc.: Academic Press (1980; Zbl 0463.60004)], H.-H. Kuo [Gaussian measures in Banach spaces, Lect. Notes Math. 463. Berlin etc.: Springer-Verlag (1975; Zbl 0306.28010)], and É. Pardoux [Équations aux dérivées partielles stochastiques non linéaires monotones. Étude de solutions forte de type Itô, Thèse d’État, Univ. Paris-Sud, Orsay (1975), see also Zbl 0363.60041] and in references therein.

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60H25 Random operators and equations (aspects of stochastic analysis)