Theorem

Girsanov's Theorem

Probability and Statistics

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

Statement

If 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

Proof Year

1960 1

Classification

Statement Form

Identity or Equation 1

Connections

Has Statement Form

Equation

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Identity

In Branch

Probability and Statistics

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

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Girsanov's Theorem

Has Statement Form

In Branch