Recently, Friedrich and Peinke demonstrated empirically that a Fokker-Planck equation describes the scale dependence of probability distribution functions of longitudinal velocity increments v(r) in fully developed turbulent flows. Thanks to the analysis of an experimental velocity signal, the stochastic process v(r) is further investigated by examining the related Langevin equation. This process is found to be Markovian in scale because the turbulent velocity field is correlated over distances much larger than the correlation length rho of its spatial derivative. A Gaussian approximation for the random force yields evolution equations for the structure functions <v(r)(n)>. Analytic solutions are obtained, in agreement with experimental data for even-order moments when the scale r is larger than a few times rho. The third-order moment <v(r)(3)> is found linear in r, as predicted by Kolmogorov's four-fifths law. (C) 2001 American Institute of Physics.