Abstract
In this chapter we shall use stochastic Taylor expansions to derive time discrete approximations with respect to the strong convergence criterion, which we shall call strong Taylor approximations. We shall mainly consider the corresponding strong Taylor schemes, and shall see that the desired order of strong convergence determines the truncation to be used. To establish the appropriate orders of various schemes we shall make frequent use of a technical lemma estimating multiple Ito integrals. This is Lemma 10.8.1, which is stated and proved in Section 8 at the end of the chapter, although it will be used earlier.
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Bibliographical Notes
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© 1992 Springer-Verlag Berlin Heidelberg
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Kloeden, P.E., Platen, E. (1992). Strong Taylor Approximations. In: Numerical Solution of Stochastic Differential Equations. Applications of Mathematics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12616-5_10
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DOI: https://doi.org/10.1007/978-3-662-12616-5_10
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