| Título: | Moments of recurrence times for Markov chains |
| Autores: |
Aurzada, Frank; TU Berlin Döring, Hanna; TU Berlin Ortgiese, Marcel; TU Berlin Scheutzow, Michael; TU Berlin |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Discrete time Markov chain, recurrence time, generalized moment 60J10 |
| Descripción: | We consider moments of the return times (or first hitting times) in an irreducible discrete time discrete space Markov chain. It is classical that the finiteness of the first moment of a return time of one state implies the finiteness of the first moment of the first return time of any other state. We extend this statement to moments with respect to a function $f$, where $f$ satisfies a certain, best possible condition. This generalizes results of K.L. Chung (1954) who considered the functions $f(n)=n^p$ and wondered "[...] what property of the power $n^p$ lies behind this theorem [...]" (see Chung (1967), p. 70). We exhibit that exactly the functions that do not increase exponentially - neither globally nor locally - fulfill the above statement. |
| Idioma: | No aplica |
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