Critical currents jc(T, H) and the flux creep rate S = dln M/dint of YBa2Cu3O7/PrBa2Cu3O7 (YBCO/PrBCO) multilayers have been measured in a wide range of temperatures T. By taking different thicknesses of the insulating PrBa2Cu3O7 layer the coupling strength between the CuO2 planes is controlled, thus making possible the crossover from 3D to the 2D regime, when the superconducting properties and the dissipation processes are strongly influenced by fluctuations. The characteristic critical temperature Tc* of the Larkin's theory for a quasi 2D superconducting layer determined from the flux creep data is in a good agreement with the Tc* value found from the magnetoresistance measurements. A strong enhancement of the quantum flux creep rate S(T → 0) has been observed in the quasi 2D YBCO/PrBCO multilayers.