Generator of an SDE diffusion
= Generator of an SDE diffusion
{title2=$L=b\cdot\nabla+\frac12\sum_k\sigma_k\sigma_k^T:D^2$}
The Itô formula identifies the operator of an SDE with drift $b$ and noise vector fields $\sigma_k$ as the displayed second-order operator. With bounded measurable coefficients, every solution satisfies the true martingale identity for $C_b^2$ test functions, hence is an <L-diffusion> in the martingale-problem sense.
// Target: probability-and-statistics.bigb