  In the present work a closed system of kinetic equations is obtained from the
truncation of the BBGKY hierarchy for the description of the vacuum creation of
an electron - positron plasma and secondary photons due to a strong laser
field. This truncation is performed in the Markovian approximation for the
one-photon annihilation channel which is accessible due to the presence of the
strong external field. Estimates of the photon production rate are obtained for
different domains of laser field parameters (frequency nu and field strength
E). A huge quantity of optical photons of the quasiclassical laser field is
necessary to satisfy the conservation laws of energy and momentum of the
constituents (e-, e+, gamma) in this channel. Since the number of these optical
photons corresponds to the order of perturbation theory, a vanishingly small
photon production rate results for the optical region and strongly subcritical
fields E << E_c. In the gamma-ray region nu <~ m the required number of laser
photons is small and the production rate of photons from the one-photon
annihilation process becomes accessible to observations for subcritical fields
E <~ E_c. In the infrared region the photon distribution has a 1/k spectrum
typical for flicker noise.
