{"title":"Persistence of one-dimensional AR(1)-processes","year":"2018","date_updated":"2022-09-12T07:52:44Z","citation":{"short":"G. Hinrichs, M. Kolb, V. Wachtel, Journal of Theoretical Probability 33 (2018) 65–102.","ama":"Hinrichs G, Kolb M, Wachtel V. Persistence of one-dimensional AR(1)-processes. <i>Journal of Theoretical Probability</i>. 2018;33:65–102. doi:<a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>","mla":"Hinrichs, Günter, et al. “Persistence of One-Dimensional AR(1)-Processes.” <i>Journal of Theoretical Probability</i>, vol. 33, Springer Science + Business Media, 2018, pp. 65–102, doi:<a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.","apa":"Hinrichs, G., Kolb, M., &#38; Wachtel, V. (2018). Persistence of one-dimensional AR(1)-processes. <i>Journal of Theoretical Probability</i>, <i>33</i>, 65–102. <a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>","bibtex":"@article{Hinrichs_Kolb_Wachtel_2018, title={Persistence of one-dimensional AR(1)-processes}, volume={33}, DOI={<a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>}, journal={Journal of Theoretical Probability}, publisher={Springer Science + Business Media}, author={Hinrichs, Günter and Kolb, Martin and Wachtel, Vitali}, year={2018}, pages={65–102} }","ieee":"G. Hinrichs, M. Kolb, and V. Wachtel, “Persistence of one-dimensional AR(1)-processes,” <i>Journal of Theoretical Probability</i>, vol. 33, pp. 65–102, 2018, doi: <a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>.","chicago":"Hinrichs, Günter, Martin Kolb, and Vitali Wachtel. “Persistence of One-Dimensional AR(1)-Processes.” <i>Journal of Theoretical Probability</i> 33 (2018): 65–102. <a href=\"https://link.springer.com/article/10.1007/s10959-018-0850-0\">https://link.springer.com/article/10.1007/s10959-018-0850-0</a>."},"language":[{"iso":"eng"}],"author":[{"last_name":"Hinrichs","full_name":"Hinrichs, Günter","first_name":"Günter"},{"first_name":"Martin","full_name":"Kolb, Martin","id":"48880","last_name":"Kolb"},{"full_name":"Wachtel, Vitali","first_name":"Vitali","last_name":"Wachtel"}],"department":[{"_id":"96"}],"publisher":"Springer Science + Business Media","publication":"Journal of Theoretical Probability","date_created":"2022-09-12T07:50:38Z","publication_status":"published","abstract":[{"lang":"eng","text":"For a class of one-dimensional autoregressive sequences (Xn), we consider the tail behaviour of the stopping time T0=min{n≥1:Xn≤0}. We discuss existing general analytical approaches to this and related problems and propose a new one, which is based on a renewal-type decomposition for the moment generating function of T0 and on the analytical Fredholm alternative. Using this method, we show that Px(T0=n)∼V(x)Rn0 for some 0<R0<1 and a positive R0-harmonic function V. Further, we prove that our conditions on the tail behaviour of the innovations are sharp in the sense that fatter tails produce non-exponential decay factors."}],"doi":"https://link.springer.com/article/10.1007/s10959-018-0850-0","user_id":"85821","page":"65–102","intvolume":"        33","volume":33,"status":"public","_id":"33335","type":"journal_article"}