Abstract
Taylor-like expansions are derived for general RODEs with Hölder continuous noise in terms of classical Taylor expansions of the vector field, followed from which general RODE-Taylor approximations are formulated. Essential RODE-Taylor approximations with minimal number of terms are determined.
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\(\Vert \cdot \Vert _2\) is the Euclidean norm of \(\mathbb {R}^d\). Throughout this book \(| \cdot |\) denotes the absolute value and also the Euclidean norm when no confusion can arise.
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Han, X., Kloeden, P.E. (2017). Taylor-Like Expansions for General Random Ordinary Differential Equations. In: Random Ordinary Differential Equations and Their Numerical Solution. Probability Theory and Stochastic Modelling, vol 85. Springer, Singapore. https://doi.org/10.1007/978-981-10-6265-0_8
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DOI: https://doi.org/10.1007/978-981-10-6265-0_8
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Online ISBN: 978-981-10-6265-0
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