Girsanov's Theorem describes how the drift of a stochastic process changes under a change of the underlying probability measure, showing that a suitable change of measure can remove a process's drift entirely, turning it into driftless Brownian motion under the new measure. Named for Igor Girsanov, it is a foundational tool of stochastic calculus widely used in mathematical finance to switch between real-world and risk-neutral pricing measures.
Facts
StatementIf Yt is a local martingale under P then the process Y tilde t = Yt minus [Y,X]t is a Q local martingale on the filtered probability space Omega, F, Q, F t to the W. 1 Classification
Statement Form Connections
Has Statement Form
In Branch
Source Girsanov theorem, Wikipedia
Sources
1. Girsanov theorem, Wikipedia
Statement section, formal formulation
if Y_t is a local martingale under P then the process Y~_t = Y_t minus [Y,X]_t is a Q local martingale on the filtered probability space Omega, F, Q, F^W_t
History section
Results of this type were first proved by Robert Horton Cameron and W. T. Martin in the 1940s and by Igor Girsanov in 1960.
In Branch: Probability and Statistics, Lead sentence
In probability theory, Girsanov's theorem or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under ch
In Group: Stochastic Processes and Martingales, Lead section
or the Cameron-Martin-Girsanov theorem explains how stochastic processes change under changes in measure. The theorem
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