  Fireball model of the gamma-ray bursts (GRBs) predicts generation of numerous
internal shocks, which efficiently accelerate charged particles and generate
relatively small-scale stochastic magnetic and electric fields. The accelerated
particles diffuse in space due to interaction with the random waves and so emit
so called Diffusive Synchrotron Radiation (DSR) in contrast to standard
synchrotron radiation they would produce in a large-scale regular magnetic
fields. In this contribution we present key results of detailed modeling of the
GRB spectral parameters, which demonstrate that the non-perturbative DSR
emission mechanism in a strong random magnetic field is consistent with
observed distributions of the Band parameters and also with cross-correlations
between them.
