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Article Dans Une Revue Journal of Statistical Physics Année : 2019

SCALING FEATURES OF TWO SPECIAL MARKOV CHAINS INVOLVING TOTAL DISASTERS

Branda Goncalves

Résumé

Catastrophe Markov chain population models have received a lot of attention in the recent past. We herewith consider two special cases of such models involving total disasters, both in discrete and in continuous-time. Depending on the parameters range, the two models can show up a recur-rence/transience transition and, in the critical case, a positive/null recurrence transition. The collapse transition probabilities are chosen in such a way that the models are exactly solvable and, in case of positive recurrence, intimately related to the extended Sibuya and Pareto-Zipf distributions whose divisibility and self-decomposability properties are shown relevant. The study includes: existence and shape of the invariant measure, time-reversal, return time to the origin, contact probability at the origin, extinction probability, height and length of the excursions, a renewal approach to the fraction of time spent in the catastrophic state, scale function, first time to collapse and first-passage times, divisibility properties.
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Dates et versions

hal-02365231 , version 1 (15-11-2019)

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  • HAL Id : hal-02365231 , version 1

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Branda Goncalves, Thierry Huillet. SCALING FEATURES OF TWO SPECIAL MARKOV CHAINS INVOLVING TOTAL DISASTERS. Journal of Statistical Physics, In press. ⟨hal-02365231⟩
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