The Girsanov theorem is a mathematical result in probability theory that relates the probability distributions of two different stochastic processes. It essentially allows for the transformation of one stochastic process into another, under certain conditions.
In finance, the Girsanov theorem is used to model and price financial derivatives, such as options and futures. It allows for the transformation of a stochastic process into a risk-neutral measure, making it easier to calculate the expected payoff of a derivative.
The Girsanov theorem assumes that the two stochastic processes being compared are continuous and have a finite variance. It also assumes that the drift and volatility of the processes are known and do not change over time.
Yes, the Girsanov theorem can be applied to non-linear processes, as long as they meet the assumptions mentioned above. However, the calculations may be more complex in these cases.
Aside from its use in finance, the Girsanov theorem has practical applications in other fields such as physics and engineering. It can be used to model and predict the behavior of complex systems, such as weather patterns or stock prices.
