確率と計量

最近stochastic calculusにかんして混乱していま。Recently, I have been confused by alternative notations for expectation and measure. E* is the risk-neutral expectation. Expectation refers to expected value, meaning sigma(i=1 to n)xi*p(xi), where p is a probability based on the risk neutral probability distribution. However, there is also a forward expectation, E^, based on a forward probability distribution p^. Interestingly, the risk neutral measure is transformed to the forward measure through the following formula: dP^/dP* = exp(integral(0 to T)rds)(NT/N0), where NT and N0 are numeraire values at T and 0. This conversion is unclear, as is the notion of "measure". It seems to the author that "measure" is basically a cumulative distribution function (CDF), as integrals over probability distributions are expressed as integral(xdP).
This conversion dP^/dP* is at the heart of the Girsanov theorem, which defines a new Brownian motion dW^ in terms of the standard Brownian motion dW.