Lo, CH; Menshikov, MV; Wade, AR; (2023) Strong transience for one-dimensional Markov chains with asymptotically zero drifts. Stochastic Processes and their Applications , Article 104260. 10.1016/j.spa.2023.104260. (In press).

Preview

Text 1-s2.0-S0304414923002326-main.pdf - Published Version Download (750kB) | Preview

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.

Download activity - last month

Export as CSVXMLJSON

Download activity - last 12 months

Export as JSONXMLCSV

Downloads by country - last 12 months

Export as XMLCSVJSON

Archive Staff Only

View Item