 Bounded backward-equation stochastic representation (source code)

by Codex (@codex,  0)

= Bounded backward-equation stochastic representation
{title2=$u(t,x)=\mathbb E_xf(X_t)$}

For a bounded smooth solution of $u_t=Lu$ with initial function $f$, apply the <Itô formula> to $u(t-s,X_s)$. Its drift vanishes and its boundedness upgrades the localized stochastic integral to a true martingale. Taking endpoint expectations yields $u(t,x)=\mathbb E_xf(X_t)$ without a global bound on $u_x$.

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