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Gauges and multigauges of stochastic processes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
(English)Article in journal (Refereed) Submitted
National Category
URN: urn:nbn:se:uu:diva-90977OAI: oai:DiVA.org:uu-90977DiVA: diva2:163523
Available from: 2003-10-21 Created: 2003-10-21 Last updated: 2013-09-25
In thesis
1. Linear and Non-linear Deformations of Stochastic Processes
Open this publication in new window or tab >>Linear and Non-linear Deformations of Stochastic Processes
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of three papers on the following topics in functional analysis and probability theory: Riesz bases and frames, weakly stationary stochastic processes and analysis of set-valued stochastic processes. In the first paper we investigate Uniformly Bounded Linearly Stationary stochastic processes from the point of view of the theory of Riesz bases. By regarding these stochastic processes as generalized Riesz bases we are able to gain some new insight into there structure. Special attention is paid to regular UBLS processes as well as perturbations of weakly stationary processes. An infinite sequence of subspaces of a Hilbert space is called regular if it is decreasing and zero is the only element in its intersection. In the second paper we ask for conditions under which the regularity of a sequence of subspaces is preserved when the sequence undergoes a deformation by a linear and bounded operator. Linear, bounded and surjective operators are closely linked with frames and we also investigate when a frame is a regular sequence of vectors. A multiprocess is a stochastic process whose values are compact sets. As generalizations of the class of subharmonic processes and the class of subholomorphic processesas introduced by Thomas Ransford, in the third paper of this thesis we introduce the general notions of a gauge of processes and a multigauge of multiprocesses. Compositions of multiprocesses with multifunctions are discussed and the boundary crossing property, related to the intermediate-value property, is investigated for general multiprocesses. Time changes of multiprocesses are investigated in the environment of multigauges and we give a multiprocess version of the Dambis-Dubins-Schwarz Theorem.

Place, publisher, year, edition, pages
Uppsala: Matematiska institutionen, 2003. 24 p.
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 29
Mathematical analysis, Riesz bases and frames, Weakly stationary stochastic processes, Set-valued analysis, Matematisk analys
National Category
Mathematical Analysis
urn:nbn:se:uu:diva-3689 (URN)91-506-1707-9 (ISBN)
Public defence
2003-11-12, 1111, Polacksbacken, Uppsala, 13:15
Available from: 2003-10-21 Created: 2003-10-21Bibliographically approved

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