Domain-wall (DW) coercive field, HCW, which characterizes pinning of DW's in soft magnetic materials, decreases strongly with increasing value of gradient, G, of the effective local DW-position-restoring magnetic field. Particular shapes of the dependence, HCW(G), can be calculated from the mean energy dissipation of the DW moving over the particular profile of the DW pinning field, Hp. In this ... [Show full abstract] paper, HCW(G) is calculated from a wall-pinning field, Hp, which is expressed as a stochastic function of the DW coordinate, xDW. The wall-pinning field, Hp, is described as a Wiener-Lévy stochastic process modified by two correlation lengths in such a way that Hp is stationary for large DW displacements and dHp/dxDW is well defined for small DW displacements. The computed HCW(G) is close to a hyperbolic decrease, but it approaches finite values if G-->0 and it decreases in a much steeper way than ~1/G for high values of G, which agrees with the experimental observations. Experimentally, the dependence HCW(G) was measured on close-packed arrays of cylindrical bubble domains in two thin films of magnetic garnets, where the local field gradient, G, was controlled within the range 109-1010 A/m2 by changing distances between neighboring DW's. The DW coercive field, HCW, extrapolated from the measured values for G-->0 was close to 80 A/m for both samples, while HCW(G~=1010 A/m2) was several times smaller. Fitting the calculated HCW(G) dependence to the experimental data, we obtained values of the Wiener-Lévy correlation lengths well comparable to the DW width parameters.