AVVISO di SEMINARIO

Prof. Nikolai Leonenko

School of Mathematics, Cardiff University, UK

TITOLO Multiscaling, Intermittency and large deviation in limit theorems for superpositions of Ornstein-Uhlenbeck type processes

Abstract Superpositions of Ornstein-Uhlenbeck type (supOU) processes provide a rich class of stationary stochastic processes for which the marginal distribution and the dependence structure may be modeled independently [1,2]. We investigate the limiting behavior of integrated supOU processes with finite variance[3,4,6] (see also [7] for multifaced behaviour of supOU processes in the case the infinite variance). We show that after suitable normalization four different limiting processes may arise. The type of limit depends on the decay of the correlation function as well as on the characteristic triplet of the marginal distribution. supOU processes, moreover, may exhibit intermittency, a phenomenon affecting the rate of growth of moments[3,4,5,6,8]. The intermittency phenomenon appears also in some other models, for example, in the subclass of ambit processes[2] known as trawl processes [5]. Joint work with D. Grahovac (Osijek University, Croatia) and M. Taqqu (Boston University, USA)

References 1. Barndorff-Nielsen, O.E. and Leonenko, N.N., (2005), Spectral properties of superpositions of Ornstein-Uhlenbeck type processes, Methodology and Computing in Applied Probability, 7, 335-352 2. Barndorff-Nielsen, O.E., Benth, F. E., Veraart, A. E.D.(2018) Ambit Stochastics, Springer. 3. Grahovac,D., Leonenko, N.,Sikorskii, A., Te?njak , I.(2016) Intermittency of superpositions of Ornstein-Uhlenbeck type processes, Journal of Statistical Physics, 165, 390-408 4. Grahovac, D., Leonenko, N., Sikorskii, A. and Taqqu.M.S. (2019) The unusual properties of aggregated superpositions of Ornstein-Uhlenbeck type processes, Bernoulli 25 (2019), no. 3, 2029?2050 5. Grahovac, D. and Leonenko, N and Taqqu, M.S.(2017) Intermittency of trawl processes, Statistic and Probability Letters, 137, 235 ? 242. 6. Grahovac, D. and Leonenko, N. and Taqqu, M.S.(2019) Limit theorems, scaling of moments and intermittency for integrated finite variance supOU processes, Stochastic Processes and Applications,129,N12,5113-5150 7. Grahovac, D. and Leonenko, N. and Taqqu, M.S.(2020) The multifaced behaviour of supOU processes: the infinite variance case, Journal of Theoretical Probability, 33, N4, 1801-1831 8. Grahovac, D. and Leonenko, N. and Taqqu, M.S. (2021) Intermittency and infinite variance: the case of integrated supOU processes, Electronic Journal of Probability, 26, art.n 56, 1-31 9. Grahovac, D. and Leonenko, N. and Taqqu, M.S. (2022) Intermittency and multiscaling in limit theorems, Fractals, 30, N 7, 2250137

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Il seminario si terrà il giorno 10 Febbraio 2023 ore 11:00 nella Aula C del Dipartimento Matematica e Applicazioni, Università di Napoli FEDERICO II, Complesso di Monte Sant'Angelo, Via Cintia, Napoli.

Link to Teams: https://teams.microsoft.com/l/meetup-join/19%3aMQ4RZDBo_0G-K_PHxKtktVYAczOGb...