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Random coefficient AR(1) process with heavy-tailed renewal-switching coefficient and heavy-tailed noise| old_uid | 938 |
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| title | Random coefficient AR(1) process with heavy-tailed renewal-switching coefficient and heavy-tailed noise |
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| start_date | 2006/03/24 |
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| schedule | 12h |
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| online | no |
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| location_info | 3e étage, salle 314 |
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| details | Invité du SAMOS-MATISSE, il propose deux exposés, prochain 31 mars, 12h |
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| summary | We discuss limit behavior of the partial sums process of stationary solution of AR(1) equation $X_t = a_t X_{t-1} + \veps_t$, with random (renewal-reward) coefficient $a_t$, taking iid\ values $A_j \in [0,1]$ on consecutive intervals of a stationary renewal process with heavy-tailed interrenewal distribution, and with iid\ innovations $\veps_t$ belonging to the domain of attraction of an $\alpha-$stable law $(0<\alpha\le 2,
\alpha \ne 1)$. Under suitable conditions on the tail parameter of the interrenewal distribution and the singularity parameter of the distribution of $A_j$ near unit root $a=1$, we show that the partial sums process of $X_t$ converges to a $\lambda-$stable Lévy process with index $\lambda<\alpha$. The paper extends the result of Leipus and Surgailis (2003) from finite variance to infinite variance $X_t$. |
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| responsibles | Carlo, Bardet, Cottrell |
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