  Consider a process, stochastic or deterministic, obtained by using a
numerical integration scheme, or from Monte-Carlo methods involving an
approximation to an integral, or a Newton-Raphson iteration to approximate the
root of an equation. We will assume that we can sample from the distribution of
the process from time 0 to finite time n. We propose a scheme for unbiased
estimation of the limiting value of the process, together with estimates of
standard error and apply this to examples including numerical integrals,
root-finding and option pricing in a Heston Stochastic Volatility model. This
results in unbiased estimators in place of biased ones i nmany potential
applications.
