Abstract
Let $\nu$ and $\mu$ be positive Radon measures on $\boldsymbol{R}^d$ in Green-tight Kato class associated with a symmetric $\alpha$-stable process $(X_t, P_x)$ on $\boldsymbol{R}^d$, and $A_t^{\nu}$ and $A_t^{\mu}$ the positive continuous additive functionals under the Revuz correspondence to $\nu$ and $\mu$. For a non-negative $\beta$, let $P_{x,t} ^{\beta \mu}$ be the law $X_t$ weighted by the Feynman-Kac functional $\exp(\beta A_t ^{\mu})$, i.e., $P_{x,t} ^{\mu} =(Z_{x,t} ^{\mu})^{-1}\exp(\beta A_t ^{\mu})P_x$, where $Z_{x, t} ^{\mu}$ is a normalizing constant. We show that $A_t ^{\nu} /t$ obeys the large deviation principle under $P_{x, t}^{\beta \mu}$. We apply it to a polymer model to identify the critical value $\beta _{\mathrm{cr}}$ such that the polymer is pinned under the law $P^{\beta \mu} _{x, t} $ if and only if $\beta$ is greater than $\beta_{\mathrm{cr}}$. The value $\beta _{\mathrm{cr}} $ is characterized by the rate function.
