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doctoral thesis
Periodic homogenization for Levy-type processes
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:462190
Valentić, Ivana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Valentić, I. (2020). Periodic homogenization for Levy-type processes (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:462190

Valentić, Ivana. "Periodic homogenization for Levy-type processes." Doctoral thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:462190

Valentić, Ivana. "Periodic homogenization for Levy-type processes." Doctoral thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:462190

Valentić, I. (2020). 'Periodic homogenization for Levy-type processes', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 27 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:462190

Valentić I. Periodic homogenization for Levy-type processes [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 27] Available at: https://urn.nsk.hr/urn:nbn:hr:217:462190

I. Valentić, "Periodic homogenization for Levy-type processes", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:462190

Metadata
TitlePeriodic homogenization for Levy-type processes
Title (croatian)Periodička homogenizacija za procese Levyjevog tipa
AuthorIvana Valentić
MentorNikola Sandrić (mentor)
Committee memberVanja Wagner (predsjednik povjerenstva)
Committee memberNikola Sandrić (član povjerenstva)
Committee memberKristina Ana Škreb (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
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.
Abstract (croatian)
Glavni cilj ove disertacije je diskutirati periodičku homogenizaciju pseudo-diferencijalnog operatora Lévyjevog tipa. Naš pristup ovom problemu bazira se na vjerojatnosnim metodama. Preciznije, kao glavni rezultat dokazujemo da odgovarajuće centriran i skaliran proces Lévyjevog tipa generiran takvim operatorom slabo konvergira prema Brownovom gibanju s kovarijacijskom matricom danom u terminima koeficijenata operatora. Posebno se koncentriramo na klasu procesa Lévyjevog tipa koji dozvoljavaju samo “male skokove” i na klasu procesa difuzija s degeneriranim difuzijskim koeficijentom. Ti rezultati generaliziraju i produbljuju klasične i dobro poznate rezultate vezane uz periodičku homogenizaciju difuzije i procesa Lévyjevog tipa u balansiranom obliku. Kako bismo razriješili ove probleme nužno je kombinirati vjerojatnosni i analitički pristup i metode, kao što su teorija semimartingala, teorija stohastičke stabilnosti i teorija integro-diferencijalnih jednadžbi.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:217:462190
Promotion2020
Study programmeTitle: Mathematics
Study programme type: university
Study level: postgraduate
Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika (doktor/doktorica znanosti, područje prirodnih znanosti, polje matematika)
Type of resourceText
Extentv, 121 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-12-04 12:57:48