Abstract
The developments that are presented in this chapter are fundamental for understanding some important tools for UQ, in particular those presented in Chapter 4 , which are devoted to the Markov Chain Monte Carlo (MCMC) methods that are a class of algorithms for constructing realizations from a probability distribution.
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Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes, North Holland, Amsterdam, 1981.
Khasminskii R. Stochastic Stability of Differential Equations, 2nd edition, Springer, 2012.
Krée P, Soize C. Mathematics of Random Phenomena, D. Reidel Publishing Company, Dordrecht, 1986 (Revised edition of the French edition Mécanique aléatoire, Dunod, Paris, 1983).
Soize C. The Fokker-Planck Equation for Stochastic Dynamical Systems and its Explicit Steady State Solutions, World Scientific Publishing Co Pte Ltd, Singapore, 1994.
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Soize, C. (2017). Markov Process and Stochastic Differential Equation. In: Uncertainty Quantification. Interdisciplinary Applied Mathematics, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-54339-0_3
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DOI: https://doi.org/10.1007/978-3-319-54339-0_3
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