Research output: Contribution to Journal/Magazine › Journal article › peer-review
<mark>Journal publication date</mark> | 08/2013 |
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<mark>Journal</mark> | Stochastic Processes and their Applications |
Issue number | 8 |
Volume | 123 |
Number of pages | 25 |
Pages (from-to) | 3027-3051 |
Publication Status | Published |
Early online date | 17/04/13 |
<mark>Original language</mark> | English |
We consider a positive recurrent Markov chain on R+ with asymptotically zero drift which behaves like -c(1)/x at infinity; this model was first considered by Lamperti. We are interested in tail asymptotics for the stationary measure. Our analysis is based on construction of a harmonic function which turns out to be regularly varying at infinity. This harmonic function allows us to perform non-exponential change of measure. Under this new measure Markov chain is transient with drift like c(2)/x at infinity and we compute the asymptotics for its Green function. Applying further the inverse transform of measure we deduce a power-like asymptotic behaviour of the stationary tail distribution. Such a heavy-tailed stationary measure happens even if the jumps of the chain are bounded. This model provides an example where possibly bounded input distributions produce non-exponential output.