Construction of gauge-invariant quantum electrodynamics in stochastic space

Gauge invariant quantum electrodynamics is constructed in the framework of the stochastic space. The $S$-matrix elements are investigated and the corrections to the anomalous magnetic moments of leptons due to stochasticity of the space are calculated. We have derived bounds for the scale of error $L\lesssim 10^{-15}$ cm which is universal constant of the dimension of length.