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Definition

Stein's Equation

Probability Theory · probability.tex
Stein's Heuristic Let $N \sim N(0,1)$. Let $h : \mathbb{R} \to \mathbb{R}$ be a Borel function such that \[ \mathbb{E}(|h(N)|) < \infty \] or in other words \[ h \in \mathcal{L}(\gamma) \] The Stein Equation associated to $h$ is the ODE \[ f'(x) -xf(x) = h(x) - \mathbb{E}(h(N)) \]
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