  We present a theory of the photovoltaic valley-dependent Hall effect in a
two-dimensional Dirac semiconductor subject to an intense near-resonant
electromagnetic field. Our theory captures and elucidates the influence of both
the field-induced resonant interband transitions and the nonequilibrium carrier
kinetics on the resulting valley Hall transport in terms of photon-dressed
quasiparticles. The non-perturbative renormalization effect of the pump field
manifests itself in the dynamics of the photon-dressed quasiparticles, with a
quasienergy spectrum characterized by {dynamical gaps $\delta_\eta$ ($\eta$ is
the valley index)} that strongly depend on field amplitude and polarization.
Nonequilibrium carrier distribution functions are determined by the pump field
frequency $\omega$ as well as the ratio of intraband relaxation time $\tau$ and
interband recombination time $\tau_{\mathrm{rec}}$. We obtain analytic results
in three regimes, when (I) all relaxation processes are negligible, (II) $\tau
\ll \tau_{\mathrm{rec}}$, and (III) $\tau \gg \tau_{\mathrm{rec}}$, and display
corresponding asymptotic dependences on $\delta_\eta$ and $\omega$. We then
apply our theory to two-dimensional transition-metal dichalcogenides, and find
a strong enhancement of valley-dependent Hall conductivity as the pump field
frequency approaches the transition energies between the pair of spin-resolved
conduction and valence bands at the two valleys.
