= Itô integrand of a finite sum of Gaussian exponentials
{c}
{title2=$f_t=\sum_jc_jh_j(t)\exp(\int_0^th_j\,dB-\tfrac12\int_0^th_j^2ds)$}
For deterministic <continuous functions> $h_j$ on a finite interval, their stochastic exponentials $M(h_j)$ are <square-integrable martingales> and satisfy $dM(h_j)=h_jM(h_j)dB$. Thus $F=\sum_jc_jM(h_j)_T$ has mean $\sum_jc_j$ and stochastic-integral representation with the displayed <integrand>. <Itô isometry> proves uniqueness up to time-probability <null sets> among square-integrable predictable integrands. It does not give pointwise uniqueness, since changing a value at one deterministic time changes no <integral>.
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