Valiukevičius, G. Estimates for the smooth functional in the classical case. (English) Zbl 0732.60061 Probability theory and mathematical statistics, Proc. 5th Vilnius Conf., Vilnius/Lith. 1989, Vol. II, 535-541 (1990). [For the entire collection see Zbl 0725.00014.] This paper deals with the distance between the martingale \(X\), written by a stochastic integral with jump part, and a solution \(Y\) of a stochastic differential equation with smooth coefficients. For a smooth functional \(F\), defined on the space \(D_{[0,T]}\) carrying the Skorokhod topology, the author estimated the mean of \(F(X)-F(Y)\), employing sensible calculations. Reviewer: Makiko Nisio (Kobe) MSC: 60G44 Martingales with continuous parameter 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) Keywords:stochastic integral with jump part; stochastic differential equation; smooth functional; Skorokhod topology Citations:Zbl 0725.00014 PDFBibTeX XML