  Focusing on the well motivated aperture mass statistics $\Map$, we study the
possibility of constraining cosmological parameters using future space based
SNAP class weak lensing missions. Using completely analytical results we
construct the covariance matrix for estimators based on two-point and
three-point statistics. Our approach incorporates an accurate modelling of
higher-order statistics to describe cosmic variance as well as various sources
of discrete noise at small angular scales. These results are then fed into a
Fisher matrix based analysis to study cosmological parameter degeneracies.
Joint and independent analysis, with or without redshift binning, for various
parameter combinations are presented. An analytical modelling of the covariance
matrix opens up the possibility of testing various approximations which are
often used in derivations of semi-analytical results. These include how
inclusion of full non-Gaussian terms in covariance matrix affects parameter
estimation. Inclusion of three-point information and how such information can
enhance the accuracy with which certain parameters can be estimated is also
studied in detail. It is shown that broad correlation structure among various
angular scales in such circumstances implies reduction in number of available
angular scales which carry completely independent information. On the other
hand, the effect of theoretical inaccuracies, in modelling either the
power-spectrum or bi-spectrum evolution, onto the measure of cosmological
parameters from weak lensing surveys is also considered. Several cosmological
parameters, $\Om$, $\sigma_8$, spectral index $n_s$, running of spectral index
$\alpha_s$ and equation of state of the dark energy $\wde$ are included in the
analysis.
