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Reflected Brownian motion on simple nested fractals

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cris.lastimport.scopus2024-02-12T20:42:43Z
dc.abstract.enFor a large class of planar simple nested fractals, we prove the existence of the reflected diffusion on a complex of an arbitrary size. Such a process is obtained as a folding projection of the free Brownian motion from the unbounded fractal. We give sharp necessary geometric conditions for the fractal under which this projection can be well defined, and illustrate them by numerous examples. We then construct a proper version of the transition probability densities for the reflected process and we prove that it is a continuous, bounded and symmetric function which satisfies the Chapman–Kolmogorov equations. These provide us with further regularity properties of the reflected process such us Markov, Feller and strong Feller property.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorKALETA, KAMIL
dc.contributor.authorPietruska-Pałuba, Katarzyna
dc.contributor.authorOlszewski, Mariusz
dc.date.accessioned2024-01-25T19:08:55Z
dc.date.available2024-01-25T19:08:55Z
dc.date.issued2019
dc.description.financeNie dotyczy
dc.description.numbernr 6, art. 1950104
dc.description.volume27
dc.identifier.doi10.1142/S0218348X19501044
dc.identifier.issn0218-348X
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/118146
dc.identifier.weblinkhttp://dx.doi.org/10.1142/s0218348x19501044
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofFractals
dc.relation.pages1-29
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.plSubordynowany ruch Browna
dc.subject.plOdbicie
dc.subject.plWłasność dobrego etykietowania
dc.subject.plProces odbijany
dc.subject.plFraktal zagnieżdżony
dc.subject.plTrójkąt Sierpińskiego
dc.subject.plWarunki brzegowe Neumanna
dc.subject.plCałkowa gęstość stanów
dc.titleReflected Brownian motion on simple nested fractals
dc.typeJournalArticle
dspace.entity.typePublication