Doléans-Dade exponential
= Doléans-Dade exponential
{c}
{title2=$\mathcal E(X)$}
{wiki}
For a continuous semimartingale $X$, its Doléans-Dade exponential is
$$
\mathcal E(X)_t=\exp\!\left(X_t-X_0-\frac12[X]_t\right).
$$
It solves $dZ_t=Z_t\,dX_t$ with $Z_0=1$.
= Stochastic exponential
{synonym}