Gaussian approximations of Brownian motion in a stochastic integral

Given a Brownian motionB, Gaussian approximationsB, >0, of the form B_t = ₀^t K (u, s)dB_sdu, t O , including polygonal and mollifier approximations, are considered. A limit theorem is proved for the integrals _T⁰X_tdB^t as O. In particular, in the case of symmetric kernelsK the limit is the Fisk-Stratonovich integral ₀^tX_t odB_t.Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Vilnius Pedagogical University, Studentu 39, 2034 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 33, No. 4, pp. 508–526, October–December, 1993.Translated by V. Mackeviius