Persistence probabilities via large deviations
Final Report Abstract
Persistence concerns the question of the probability that a stochastic process has an unusually long excursion. The rate of decay of this probability is governed by a persistence exponent. This type of question is a classical question in probability theory. It is considered very hard; and despite high recent activity in the field, general methods are not available. Contrary to the latter, large deviation theory is a well-developed subject. The new angle of attack of the project was in applying large deviation theory techniques to persistence type problems. It turned out that the explicit reformulation of persistence problems in the large deviation language is possible, but that the gain from it is small. In spite of this, we could successfully use ideas from large deviation theory to advance the knowledge of persistence type problems. The project was pursued in joint work with Christophe Profeta (Évry) as well as Sumit Mukherjee (Columbia) and Ofer Zeitouni (Weizman Institute).
Publications
- Persistence exponents via perturbation theory: AR(1)-processes. Journal of Statistical Physics 177 (2019), 651–665
Frank Aurzada and Marvin Kettner
(See online at https://doi.org/10.1007/s10955-019-02384-3) - Persistence exponents in Markov chains. Annales de l’Institut Henri Poincaré - Probabilités et Statistiques 57 (2021), 1411–1441
Frank Aurzada, Sumit Mukherjee, Ofer Zeitouni
(See online at https://doi.org/10.1214/20-AIHP1114) - Persistence exponents via perturbation theory: autoregressive and moving average processes. PhD thesis. 2021
Marvin Kettner
(See online at https://dx.doi.org/10.26083/tuprints-00017566)
