Doléans-Dade exponential
From Wikipedia, the free encyclopedia
In stochastic calculus, the Doléans-Dade exponential or stochastic exponential of a semimartingale X is the unique strong solution of the stochastic differential equation
where denotes the process of left limits, i.e., .
The concept is named after Catherine Doléans-Dade.[1] Stochastic exponential plays an important role in the formulation of Girsanov's theorem and arises naturally in all applications where relative changes are important since measures the cumulative percentage change in .