Note on Wagner-Platen's representation of solutions of a general filtering stochastic differential equation (Q1063945)

The author considers the stochastic vector differential equation \[ (*)\quad x_ t=x_{t_ 0}+\int^{t}_{t_ 0}a(u,x_ u)du+\int^{t}_{t_ 0}b(u,x_ u)dw_ u+\int^{t}_{t_ 0}c(u,x_ u)dY_ u,\quad t\in [t_ 0,T], \] where \(w_ t\) is a standard vector Wiener process and \(Y_ t=N_ t-t\), \(N_ t\) being a standard vector Poisson process independent of \(w_ t\). Usual assumptions for the existence and uniqueness of (*) are made. The author shows that such a solution can be represented by a stochastic generalization of Taylor's formula due to \textit{W. Wagner} and \textit{E. Platen} [see: Approximation of Itô integral equations. (Preprint) Akademie der Wissenschaften der DDR, Zentralinstitut für Mathematik und Mechanik (1978; Zbl 0413.60056) see also \textit{E. Platen}, (Preprint) Vilnus, Inst. Math. Cypern., Acad. Sci. Lith. SSR. (1980))].