New semigroups from old: An approach to Feller boundary conditions
Artykuł w czasopiśmie
MNiSW
70
Lista 2024
| Status: | |
| Autorzy: | Bobrowski Adam |
| Dyscypliny: | |
| Aby zobaczyć szczegóły należy się zalogować. | |
| Rok wydania: | 2024 |
| Wersja dokumentu: | Drukowana | Elektroniczna |
| Język: | angielski |
| Numer czasopisma: | 5-6 |
| Wolumen/Tom: | 17 |
| Strony: | 2108 - 2140 |
| Impact Factor: | 1,3 |
| Web of Science® Times Cited: | 0 |
| Scopus® Cytowania: | 0 |
| Bazy: | Web of Science | Scopus |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | TAK |
| Licencja: | |
| Sposób udostępnienia: | Otwarte czasopismo |
| Wersja tekstu: | Ostateczna wersja opublikowana |
| Czas opublikowania: | W momencie opublikowania |
| Data opublikowania w OA: | 2 maja 2024 |
| Abstrakty: | angielski |
| Stochastic techniques allow constructing new random processes from old. For example, given an unrestricted Brownian motion one can con- struct reflecting, elastic, killed, and stopped Brownian motions. On the other hand, from the functional-analytic point of view, the semigroups that describe these new processes seem to need to be obtained independently, using the Hille–Yosida theorem. The aim of this article is to show that this is not nec- essary; all these semigroups are hidden in the unrestricted Brownian motion semigroup as its subspace semigroups. In other words, in the semigroup the- ory, subspace semigroups play the role of a number of advanced techniques of stochastic analysis. To exemplify this, we exhibit a number of invariant subspaces for the unre- stricted Brownian motion semigroup, construct the corresponding semigroups and show how they are related to the semigroups describing Brownian motions on the half-line with various types of boundary behavior at x = 0, including the Brownian motions named above. This analysis is then applied to explain- ing the nature of transmission conditions used in modeling semi-permeable and permeable membranes. |
