The stochastic inversion theory, formulated on stochastic processes and defined on real Hilbert spaces, has been utilized in the optimal solution to inverse the global geomagnetic sounding (GMS) problem to estimate vertical conductivity distribution of the Earth from long period geomagnetic continuum data in the bandwidth 0.2-0.01 cycles per day (CPD). The stochastic formalism, in essence, is based upon an iterative perturbation algorithm, which relates the changes in the model to first order changes in the data affected through the imposition of first order Taylor series expansion about some a priori/updated model parameters at frequencies and degrees of spherical harmonics. This approximation reduces the nonlinear GMS inversion problem to solving a system of linear perturbation equations, which are simultaneously underdetermined and overconstrained. The system of linear perturbation equations gets solved through the application of a stochastic inversion formula and the computed perturbations are added to the a priori/updated model parameters. This calculation sequence keeps iterating till an optimal model results (hopefully), satisfying a reduced chi-square statistic criterion, an indicator of goodness of fit test between observed GMS data and the theoretical data functionals corresponding to a finally accepted model. For the envisaged layered Earth structure, a priori resistivities and thicknesses alongwith noise and solution autocorrelation operators are required to initiate the stochastic inversion algorithm. Computer-assisted interactive forward modeling, corresponding to frequencies belonging to the mentioned frequency band and a spherical harmonic of degree one, has been undertaken to estimate a priori layer parameters. Fidelity of the estimated parameters in terms of parameter resolutions and total estimation error involved in respect of parameter estimations have also been studied in their entireties. Correlation coefficients of the estimated parameters have also been provided. Starting with a priori layer parameters, obtained by computer-assisted interactive modeling, stochastic inversion has been successful in retrieving the resistivity-depth distribution of the Earth from a depth of about 436.19±7.81 km from the Earth’s surface with a resistivity low of 0.96±0.08 ohm◊m, which gets further reduced to 0.86±0.16 ohm◊m at a depth of 565.0±11.9 km which continues down to a depth of 845.62±17.74 km approximately with satisfactory parameter resolutions and minimum total estimation errors. Correlation coefficients of the estimated parameters are mostly characterized by zeroes/small values, indicating insignificant parameter correlations. The agreement between the observed data and the corresponding best-fit curve is finally obtained for a reduced chi-square statistic criterion less than unity. Non-retrieval of resistivity-depth distribution in respect of the upper surface and conducting interior of the Earth is mostly caused by inadequate data bandwidth and noisy data, as actually available, utilized in the inversion process.