 Strong transience for one-dimensional Markov chains with asymptotically zero driftsChak Hei Lo, Mikhail V. Menshikov and Andrew R. Wade Stochastic Processes and their Applications, 2024, vol. 170, issue C Abstract: For near-critical, transient Markov chains on the non-negative integers in the Lamperti regime, where the mean drift at x decays as 1/x as x→∞, we quantify degree of transience via existence of moments for conditional return times and for last exit times, assuming increments are uniformly bounded. Our proof uses a Doob h-transform, for the transient process conditioned to return, and we show that the conditioned process is also of Lamperti type with appropriately transformed parameters. To do so, we obtain an asymptotic expansion for the ratio of two return probabilities, evaluated at two nearby starting points; a consequence of this is that the return probability for the transient Lamperti process is a regularly-varying function of the starting point. Keywords: Transience; Lamperti problem; Last exit times; Conditional return times; Doob transform; Return probabilities (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:170:y:2024:i:c:s0304414923002326 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2023.104260 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.