Typical Martingale Diverges at a Typical Point

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10331927" target="_blank" >RIV/00216208:11320/16:10331927 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10959-014-0567-7" target="_blank" >http://dx.doi.org/10.1007/s10959-014-0567-7</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10959-014-0567-7" target="_blank" >10.1007/s10959-014-0567-7</a>

Result language
angličtina
Original language name
Typical Martingale Diverges at a Typical Point
Original language description
We investigate convergence of martingales adapted to a given filtration of finite alpha-algebras. To any such filtration, we associate a canonical metrizable compact space K such that martingales adapted to the filtration can be canonically represented on K. We further show that (except for trivial cases) typical martingale diverges at a comeager subset of K. 'Typical martingale' means a martingale from a comeager set in any of the standard spaces of martingales. In particular, we show that a typical L-1-bounded martingale of norm at most one converges almost surely to zero and has maximal possible oscillation on a comeager set.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F12%2F0290" target="_blank" >GAP201/12/0290: Topological and geometrical properties of Banach spaces and operator algebras</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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