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Markov Process and Stochastic Differential Equation

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Part of the book series: Interdisciplinary Applied Mathematics ((IAM,volume 47))

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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References

  1. Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes, North Holland, Amsterdam, 1981.

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  2. Khasminskii R. Stochastic Stability of Differential Equations, 2nd edition, Springer, 2012.

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  3. 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).

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  4. 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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