Girsanov theorem

Girsanov theorem describes how changing probability measure transforms the drift of a stochastic process. For Brownian motion, a suitable change of measure adds a drift while preserving Brownian behavior under the new measure.

Radon–Nikodym derivative: A function that expresses one measure as a density relative to another. Its stochastic exponential weights paths to define the new probability measure.
Risk-neutral measure: A probability measure under which discounted asset prices are martingales in a financial model. Girsanov can change a model's asset drift to the risk-neutral drift.
Probability measure: A measure assigning total mass one to the events of a probability space. Girsanov compares two probability measures on the same underlying space.
Dambis–Dubins–Schwarz theorem: A theorem representing a continuous local martingale as Brownian motion run on its quadratic-variation clock. It changes the time parametrization, whereas Girsanov changes the probability measure.
Exponential martingale: A stochastic exponential that is a martingale under suitable integrability conditions. It commonly supplies the density process used in the theorem.
Black–Scholes model: A model of option prices based on geometric Brownian motion and no-arbitrage assumptions. A measure change converts the stock's physical drift to its risk-neutral drift for pricing.
Filtration: An increasing family of sigma-algebras representing information available over time. The density process and drift must respect the information available at each time.
Time change: A transformation that reparametrizes a stochastic process using a random or deterministic clock. Time change can alter apparent dynamics without the measure change central to Girsanov.
Brownian motion: A continuous-time stochastic process with independent Gaussian increments and continuous paths. The theorem changes its drift under a new measure without changing its Brownian character.
Feynman–Kac formula: A representation of solutions to certain partial differential equations as expectations of stochastic processes. Changing drift can align the process in the expectation with the equation's differential operator.

Linked from 2 pages

Radon–Nikodym theoremBroader topic: Its measure changes are implemented through Radon–Nikodym derivatives.