Naslov
Periodic homogenization for Levy-type processes
(Periodička homogenizacija za procese Levyjevog tipa)

Autori
Valentić, Ivana

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Prirodoslovno-matematički fakultet - Matematički odsjek

Mjesto
Zagreb

Datum
01.01

Godina
2020

Stranica
V, 121

Mentor
Sandrić, Nikola

Ključne riječi
Brownian motion ; Lévy-type process ; semimartingales
(Brownovo gibanje ; proces Lévyjevog tipa ; semimartingali)

Sažetak
The main goal of this thesis is to discuss periodic homogenization of a Lévy-type pseudodifferential operator. Our approach to this problem is based on probabilistic techniques. More precisely, as the main result we show that the appropriately centered and scaled Lévy-type process (LTP) generated by this operator converges weakly to a Brownian motion with covariance matrix given in terms of the operator coefficients. We specially focus on a class of Lévy-type processes admitting “small jumps” only and a class of diffusion processes having degenerate diffusion term. These results generalize and refine the classical and well-known results related to periodic homogenization of diffusion process and of Lévy-type process in balanced form. In order to resolve these problems, it is necessary to combine both probabilistic and analytical approaches and tools, such as theory of semimartingales, stochastic stability theory and theory of integro-differential equations.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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