Details

Autor(en) / Beteiligte

• Goncalves, Branda
• Huillet, Thierry

Titel

Scaling Features of Two Special Markov Chains Involving Total Disasters

Ist Teil von

• Journal of statistical physics, 2020-01, Vol.178 (2), p.499-531

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2020

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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 recurrence/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.