Abstract
A brief, heuristic introduction into stochastic integration and stochastic differential equations is given in this chapter, as well a derivation of stochastic Taylor expansions.
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Literature for Chapter 2
There are many books which introduce the theory of stochastic differential equations such as Gikhman & Skorokhod (1972). Arnold (1974), Øksendal (1985) and Gard (1988). More advanced treatments are provid ed e.g. by Ikeda & Watana.be (1981, 89), Kar atzas & Shreve (1988) or Protter (1990). First results on the Ito-Taylor formula can be found in Wagner & Platen (1978) and Platen & Wagner (1982). Azencott (1982) gener alized thi s. The StratonovichTaylor formula was given in Kloed en & Platen (I!J91a). Both are derived in Kloed en & Platen (1992a). Approximations on multipl e stochastic integ rals ar e considered in Liske, Platen & Wagner (1982), Milstein (1988a) an d Kloeden, Platen & Wright (1992). Relations between multipl e Ito-and Stratonovich integrals are considered in Kloeden & Platen (1991b).
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© 1994 Springer-Verlag Berlin Heidelberg
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Kloeden, P.E., Platen, E., Schurz, H. (1994). Stochastic Differential Equations. In: Numerical Solution of SDE Through Computer Experiments. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57913-4_2
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DOI: https://doi.org/10.1007/978-3-642-57913-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57074-5
Online ISBN: 978-3-642-57913-4
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