Random Ordinary Differential Equations and Their Numerical Solution
This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely
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Xiaoying Han Peter E. Kloeden
Random Ordinary Differential Equations and Their Numerical Solution
Probability Theory and Stochastic Modelling Volume 85
Editors-in-chief Søren Asmussen, Aarhus, Denmark Peter W. Glynn, Stanford, CA, USA Yves Le Jan, Orsay, France Advisory Board Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Andreas Kyprianou, Bath, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, BC, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences
More information about this series at http://www.springer.com/series/13205
Xiaoying Han Peter E. Kloeden •
Random Ordinary Differential Equations and Their Numerical Solution
123
Xiaoying Han Auburn, AL USA
Peter E. Kloeden School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan, Hubei China
ISSN 2199-3130 ISSN 2199-3149 (electronic) Probability Theory and Stochastic Modelling ISBN 978-981-10-6264-3 ISBN 978-981-10-6265-0 (eBook) DOI 10.1007/978-981-10-6265-0 Library of Congress Control Number: 2017951158 Mathematics Subject Classification (2010): 37H10, 60H10, 60H35, 34F05, 37H70, 60H30, 65LC30, 65L05, 65L06, 65L20, 92-08 © Springer Nature Singapore Pte Ltd. 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction o
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