Girsanovs

Girsanovs is a Slavic surname. In academic contexts the name is most often encountered through the attribution to Girsanov’s theorem, a foundational result in probability theory. The theorem, named after Igor V. Girsanov, describes how the probability measure governing a stochastic process can be changed so that the process has a different drift, typically turning a Brownian motion with drift into a Brownian motion under a new measure. The construction uses a Radon-Nikodym derivative given by an exponential martingale. The result requires certain integrability conditions to ensure the new measure is well defined. In essence, Girsanov’s theorem provides a tool to adjust drift terms by changing the underlying probability measure, a key technique in stochastic calculus.

Applications and context: The theorem underpins risk-neutral valuation in financial mathematics, enabling derivative pricing by working under a measure in which asset prices follow martingale dynamics. It also informs filtering theory and various models of stochastic differential equations.

Notable people: The surname Girsanovs may refer to individuals bearing the name; the most prominent figure linked to the theorem is Igor V. Girsanov.

See also: Girsanov’s theorem; stochastic calculus; change of measure; Radon-Nikodym derivative; Brownian motion.