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Stratonovich and Itô stochastic Taylor expansions. (English) Zbl 0731.60050
For the solution \(X_ t\) of stochastic differential equations where the stochastic integral is interpreted in the sense of Stratonovich the Taylor expansion of \(f(x_ t)\) for general functions f is stated and proved.

60H05 Stochastic integrals
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[1] Arous, Prob. Theory and Rel. Fields 81 pp 29– (1989)
[2] (1982), Formule de Taylor stochastique et developpement asymptotique d’integrales de Feynmann. Springer Lecture Notes in Mathematics, Volume 921, pp. 237–285
[3] and (1988), Sur les integrales multiple de Stratonovich, Springer Lecture Notes in Mathematics, Volume 1321, pp. 72–81
[4] and (1981), Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam
[5] Kloeden, Stochastic Hydrol. Hydraul. 3 pp 155– (1989)
[6] and (1991), The Numerical Solution of Stochastic Differential Equations, Springer Verlag (Series Applications of Mathematics)
[7] (1982). A generalized Taylor formula for solutions of stochastic equations, Sankhya A 44, 163–172 · Zbl 0586.60049
[8] Platen, Prob. Math. Stat. 3 pp 37– (1982)
[9] (1988), Product expansions of exponential Lie series and the discretization of stochastic differential equations, in Stochastic Differential Systems, Stochastic Control Theory, and Applications, edited by and , Springer IMA Series, Volume 10, pp. 563–582
[10] and (1978), Approximation of Ito integral equations, Preprint, Zentralinstitut für Mathematik und Mechanik, Akademie der Wissenschaften der DDR, Berlin, 27 pages
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