Shift-invariant measures on infinite-dimensional spaces: Integrable functions and random walks
Averaging of random shift operators on a space of the square integrable by shift-invariant measure complex-valued functions on linear topological spaces has been studied. The case of the l∞ space has been considered as an example. A shift-invariant measure on the l∞ space, which was constructed b...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2018-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/shift-invariant-measures-on-infinite-dimensional-403659.html |
| Summary: | Averaging of random shift operators on a space of the square integrable by shift-invariant measure complex-valued functions on linear topological spaces has been studied. The case of the l∞ space has been considered as an example.
A shift-invariant measure on the l∞ space, which was constructed by Caratheodory's scheme, is σ-additive, but not σ-finite. Furthermore, various approximations of measurable sets have been investigated. One-parameter groups of shifts along constant vector fields in the l∞ space and semigroups of shifts to a random vector, the distribution of which is given by a collection of the Gaussian measures, have been discussed. A criterion of strong continuity for a semigroup of shifts along a constant vector field has been established.
Conditions for collection of the Gaussian measures, which guarantee the semigroup property and strong continuity of averaged one-parameter collection of linear operators, have been defined. |
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| ISSN: | 2541-7746 2500-2198 |