# Persistence Exponents via Perturbation Theory: AR(1)-Processes

@article{Aurzada2019PersistenceEV, title={Persistence Exponents via Perturbation Theory: AR(1)-Processes}, author={Frank Aurzada and Marvin Kettner}, journal={Journal of Statistical Physics}, year={2019} }

For AR(1)-processes $X_n=\rho X_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\in\mathbb{N}}$ is an i.i.d. sequence of random variables, we study the persistence probabilities $\mathbb{P}(X_0\ge 0,\dots, X_N\ge 0)$ for $N\to\infty$. For a wide class of Markov processes a recent result [Aurzada, Mukherjee, Zeitouni; arXiv:1703.06447; 2017] shows that these probabilities decrease exponentially fast and that the rate of decay can be identified as an eigenvalue of some…

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