Abstract: IJ orem: Let \left\X_n, n>1\right\ be a Guassian random variable sequence centered at expectetions. Assume that uniformly in m \begingathered E\left(\sum_k=m+1^w+n X_k\right)^2 \gg n, \quad E X_k^2 \ll 1 \\ S_t=S(t)=\sum_k< 1 X_k, \quad t \geqslant 0 \\ a_t-E S_t^2, \quad \rho(n)=\sup _\mathrmm\left|E X_\mathrmm X_\mathrmm+\mathrmm\right| \endgathered Put Suppose- that for some constants C(\geqslant 1), \lambda>0 \rho(n) \leqslant C n^-3 / 2-\lambda then, without changing the distribution of \S(t), t \geqslant 0\, we can redefine the proecss \S(t), 1 \geq 0\ on a richer probability space together with a standard Wiener process \left\W^\prime(l),: \geqslant 0\right\ such that \beginaligned & S(t)-W\left(b_t\right) \ll \log ^\frac12 t \quad \text a.s. \\ & b_t \approx a_t+r_t, \quad r_t \ll \sum_k< i k^-\frac12-x. \endaligned where.