  We discuss a new approach of scalar field theory where the small field
contributions are treated perturbatively and the large field configurations
(which are responsible for the asymptotic behavior of the perturbative series)
are neglected. In two Borel summable lambda phi ^4 problems improved
perturbative series can be obtained by this procedure. The modified series
converge towards values exponentially close to the exact ones. For lambda
larger than some critical value, the method outperforms Pade approximants and
Borel summations. The method can also be used for series which are not Borel
summable such as the double-well potential series and provide a perturbative
approach of the instanton contribution. Semi-classical methods can be used to
calculate the modified Feynman rules, estimate the error and optimize the field
cutoff. We discuss Monte Carlo simulations in one and two dimensions which
support the hypothesis of dilution of large field configurations used in these
semi-classical calculations. We show that Monte Carlo methods can be used to
calculate the modified perturbative series.
