%0 Book %1 lord2014introduction %A Lord, Gabriel J. %A Powell, Catherine E. %A Shardlow, Tony %B Cambridge Texts in Applied Mathematics %C Cambridge %D 2014 %I Cambridge University Press %K 60-01-probability-instructional-exposition 60-04-probability-theory-software-source-code 60g10-stationary-stochastic-processes 60hxx-stochastic-analysis 65-02-numerical-analysis-research-exposition 65c30-numerical-solutions-to-stochastic-and-integral-differential-equations 65n30-pdes-bvps-finite-elements 65n35-pdes-bvps-spectral-collocation-and-related-methods %R DOI: 10.1017/CBO9781139017329 %T An Introduction to Computational Stochastic PDEs %U https://www.cambridge.org/core/books/an-introduction-to-computational-stochastic-pdes/01A784303F5C86644A25BFB138923090 %X This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science. %@ 9780521899901

@book{lord2014introduction, abstract = {This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB® codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.}, added-at = {2022-03-20T01:27:01.000+0100}, address = {Cambridge}, author = {Lord, Gabriel J. and Powell, Catherine E. and Shardlow, Tony}, biburl = {https://www.bibsonomy.org/bibtex/2134d6bb30ac5ee91c2832b18bde0655e/gdmcbain}, booktitle = {Cambridge Texts in Applied Mathematics}, description = {An Introduction to Computational Stochastic PDEs}, doi = {DOI: 10.1017/CBO9781139017329}, interhash = {466daf13d8c05d71adeb409490dcc234}, intrahash = {134d6bb30ac5ee91c2832b18bde0655e}, isbn = {9780521899901}, keywords = {60-01-probability-instructional-exposition 60-04-probability-theory-software-source-code 60g10-stationary-stochastic-processes 60hxx-stochastic-analysis 65-02-numerical-analysis-research-exposition 65c30-numerical-solutions-to-stochastic-and-integral-differential-equations 65n30-pdes-bvps-finite-elements 65n35-pdes-bvps-spectral-collocation-and-related-methods}, publisher = {Cambridge University Press}, timestamp = {2022-03-20T01:28:18.000+0100}, title = {An Introduction to Computational Stochastic PDEs}, url = {https://www.cambridge.org/core/books/an-introduction-to-computational-stochastic-pdes/01A784303F5C86644A25BFB138923090}, year = 2014 }