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doctoral thesis
Subordinate random walks
Zagreb: University of Zagreb, Faculty of Science, 2019. urn:nbn:hr:217:924439
Šebek, Stjepan
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Šebek, S. (2019). Subordinate random walks (Doctoral thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:924439

Šebek, Stjepan. "Subordinate random walks." Doctoral thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:924439

Šebek, Stjepan. "Subordinate random walks." Doctoral thesis, University of Zagreb, Faculty of Science, 2019. https://urn.nsk.hr/urn:nbn:hr:217:924439

Šebek, S. (2019). 'Subordinate random walks', Doctoral thesis, University of Zagreb, Faculty of Science, accessed 19 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:924439

Šebek S. Subordinate random walks [Doctoral thesis]. Zagreb: University of Zagreb, Faculty of Science; 2019 [cited 2024 December 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:924439

S. Šebek, "Subordinate random walks", Doctoral thesis, University of Zagreb, Faculty of Science, Zagreb, 2019. Available at: https://urn.nsk.hr/urn:nbn:hr:217:924439

Metadata
TitleSubordinate random walks
Title (croatian)Subordinirane slučajne šetnje
AuthorStjepan Šebek
MentorZoran Vondraček (mentor)
Committee memberBojan Basrak (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 country2019-05-16, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Universal decimal classification
(UDC)		51 - Mathematics
Abstract
In this thesis, we consider a large class of subordinate random walks on the integer lattice \(\mathbb{Z}^d\) via subordinators with Laplace exponents which are complete Bernstein functions satisfying some mild scaling conditions at zero. Subordination is a procedure for obtaining new process from the original one. The new process may differ very much from the original process, but the properties of this new process can be understood in terms of the original process. Main results of the thesis are the elliptic Harnack inequality and n-step transition probability estimates for subordinate random walks. In order to obtain the elliptic Harnack inequality, we first establish estimates for one-step transition probabilities, the Green function and the Green function of a ball. The main tools we apply to get \(n\)-step transition probability estimates for subordinate random walks are the parabolic Harnack inequality and appropriate bounds for the transition kernel of the corresponding continuous time random walk.
Abstract (croatian)
U ovoj disertaciji promatramo veliku klasu subordiniranih slučajnih šetnji na cjelobrojnoj mreži \(\mathbb{Z}^d\) dobivenih pomoću subordinatora s Laplaceovim eksponentima koji su potpune Bernsteinove funkcije koje zadovoljavaju neke blage uvjete skaliranja u nuli. Subordinacija je procedura dobivanja novog procesa na temelju originalnog procesa. Iako se novi proces može dosta razlikovati od originalnog, svojstva dobivenog procesa mogu se shvatiti u terminima originalnog procesa. Glavni rezultati do kojih dolazimo su eliptička Harnackova nejednakost te ocjene na prijelazne vjerojatnosti za subordinirane slučajne šetnje. Kako bismo dobili eliptičku Harnackovu nejednakost, prvo dokazujemo ocjene za jednokoračne prijelazne vjerojatnosti, Greenovu funkciju te Greenovu funkciju kugle. Glavne tehnike koje koristimo kako bismo dobili ocjene za \(n\)-koračne prijelazne vjerojatnosti za subordinirane slučajne šetnje su parabolička Harnackova nejednakost i odgovarajuće ocjene za prijelaznu jezgru pripadajuće neprekidno vremenske slučajne šetnje.
Keywords
Keywords (english)
Languageenglish
URN:NBNurn:nbn:hr:217:924439
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, 86 str.
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-05-28 11:21:28