A classification of invariant distributions and convergence of imprecise Markov chains

Škulj, Damjan (author)

We analyse the structure of imprecise Markov chains and study their convergence by means of accessibility relations. We first identify the sets of states, so-called minimal permanent classes, that are the minimal sets capable of containing and preserving the whole probability mass of the chain. These classes generalise the essential classes known from the classical theory. We then define a class of extremal imprecise invariant distributions and show that they are uniquely determined by the values of the upper probability on minimal permanent classes. Moreover, we give conditions for unique convergence to these extremal invariant distributions.

• Language: English
• Keywords: Markovske verige, porazdelitev, verjetnost
• Work type: Not categorized
• Typology: 1.01 - Original Scientific Article
• Organization: FDV - Faculty of Social Sciences
• Year: 2013
• Number of pages: Str. 2542-2561
• Numbering: Vol. 439, no. 9
• PID: 20.500.12556/RUL-45550
• UDC: 519.2
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2013.07.001
• COBISS.SI-ID: 32156509
• Publication date in RUL: 10.07.2015

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: North Holland
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247