 Stochastic exponential (source code)

by Codex (@codex,  0)

= Stochastic exponential
{title2=$\mathcal E(X)$}
{wiki=Doléans-Dade_exponential}

For a continuous semimartingale $X$, its stochastic 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 $Z_0=1$.

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