  Recent well resolved numerical simulations of AGN feedback have shown that
its effects on the host galaxy may be not only negative but also positive. In
the late gas poor phase, AGN feedback blows the gas away and terminates star
formation. However, in the gas-rich phase(s), AGN outflows trigger star
formation by over-compressing cold dense gas and thus provide positive feedback
on their hosts. In this paper we study this AGN-triggered starburst effect. We
show that star formation rate in the burst increases until the star formation
feedback counteracts locally the AGN outflow compression. Globally, this
predicts a strong nearly linear statistical correlation between the AGN and
starburst bolometric luminosities in disc galaxies, L_* \propto L_{AGN}^{5/6}.
The correlation is statistical only because AGN activity may fluctuate on short
time scales (as short as tens of years), and because AGN may turn off but its
effects on the host may continue to last until the AGN-driven outflow leaves
the host, which may be up to 10 times longer than the duration of the AGN
activity. The coefficient in front of this relation depends on the clumpiness
and morphology of the cold gas in the galaxy. A "maximum starburst" takes place
in am azimuthally uniform gas disc, for which we derive an upper limit of L_*
\sim 50 times larger than L_{AGN} for typical quasars. For more clumpy and/or
compact cold gas distributions, the starburst luminosity decreases. We also
suggest that similar AGN-triggerred starbursts are possible in hosts of all
geometries, including during galaxy mergers, provided the AGN is activated.
Finally, we note that due to the short duration of the AGN activity phase the
accelerating influence of AGN on starbursts may be much more common than
observations of simultaneous AGN and starbursts would suggest.
