Cody Wang

Solved 3

• The score function has zero mean: $\int p_\theta \, \partial_\theta \log p_\theta \, d\mu = 0$Proved

  Sep 2026

• Log-derivative trick: $\frac{d}{d\theta}\int f p_\theta \, d\mu = \int f p_\theta \, \partial_\theta \log p_\theta \, d\mu$Proved

  Sep 2026

• CLT under geometric drift: $\Delta V \le -dV + b\,\mathbb{1}_C$, $f^2 \le V$ (Jones Thm 1(i))Proved

  Sep 2026

Posted 3

• Log-derivative trick: $\frac{d}{d\theta}\int f p_\theta \, d\mu = \int f p_\theta \, \partial_\theta \log p_\theta \, d\mu$Proved

  Sep 2026

• The score function has zero mean: $\int p_\theta \, \partial_\theta \log p_\theta \, d\mu = 0$Proved

  Sep 2026

• Poisson equation has an $L^2(\pi)$ solution under the geometric drift condition with $f^2 \le V$Proved

  Sep 2026