| Abstract: |
| We characterize quasi-ergodic limiting measures for additive functionals of a symmetric Markov process $X$. We consider two types of additive functionals beyond the classical occupation-time setting: continuous additive functionals associated with Revuz measures and purely discontinuous additive functionals. Our results do not require the finiteness of the total mass of the underlying measure nor (intrinsic) ultracontractivity of the semigroups, assumptions commonly imposed in the existing literature. As a consequence, we establish Chacon-Ornstein type ratio ergodic limits for additive functionals of $X$. |
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