  Detection of solar gravity modes remains a major challenge to our
understanding of the innerparts of the Sun. Their frequencies would enable the
derivation of constraints on the core physical properties while their
amplitudes can put severe constraints on the properties of the inner convective
region. Our purpose is to determine accurate theoretical amplitudes of solar g
modes and estimate the SOHO observation duration for an unambiguous detection.
We investigate the stochastic excitation of modes by turbulent convection as
well as their damping. Input from a 3D global simulation of the solar
convective zone is used for the kinetic turbulent energy spectrum. Damping is
computed using a parametric description of the nonlocal time-dependent
convection-pulsation interaction. We then provide a theoretical estimation of
the intrinsic, as well as apparent, surface velocity. Asymptotic g-mode
velocity amplitudes are found to be orders of magnitude higher than previous
works. Using a 3D numerical simulation, from the ASH code, we attribute this to
the temporal-correlation between the modes and the turbulent eddies which is
found to follow a Lorentzian law rather than a Gaussian one as previously used.
We also find that damping rates of asymptotic gravity modes are dominated by
radiative losses, with a typical life-time of $3 \times 10^5$ years for the
$\ell=1$ mode at $\nu=60 \mu$Hz. The maximum velocity in the considered
frequency range (10-100 $\mu$Hz) is obtained for the $\ell=1$ mode at $\nu=60
\mu$Hz and for the $\ell=2$ at $\nu=100 \mu$Hz. Due to uncertainties in the
modeling, amplitudes at maximum i.e. for $\ell=1$ at 60 $\mu$Hz can range from
3 to 6 mm s$^{-1}$.
