Girsanov's theorem describes how a change of probability measure changes the drift of a semimartingale. If the appropriate stochastic exponential is a true martingale, weighting by it turns into a Brownian motion under the new measure.
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Girsanov's theorem is a fundamental result in the theory of stochastic processes, particularly in the field of stochastic calculus and quantitative finance. It provides a way to change the probability measure under which a stochastic process is defined, transforming it into another process that may have different characteristics. This is particularly useful in financial mathematics for pricing derivatives and in risk management. ### Key Concepts: 1. **Stochastic Processes**: A stochastic process is a collection of random variables indexed by time or space.