Exponential Decay Parameters Associated with Excessive Measures

Abstract

Let X be a Markov process with semigroup (P _t ) and m an excessive measure of X. With m we associate the spectral radius $\lambda_r^{(p)}(m)$ of (P _t ) on $L^p(m) \ (1\leq p\leq \infty )$ and the exit parameter $\lambda_e^{\mathcal{C}}(m)$ defined for an m-nest $\mathcal{C = }(C_n)$ in terms of the corresponding first exit times $(\tau_n)$. We discuss the impact of these parameters as well as their connection with other parameters of interest for the process.