컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0630 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Probability / Stochastic Process / Statistics (SS-12) |
| 영문제목 (Title(Eng.)) |
Ergodicity and asymptotic stability of Feller semigroups on Polish spaces |
| 저자(Author(s)) |
Fuzhou Gong1 Chinese Academy of Sciences1 |
| 초록본문(Abstract) | There exists a long literature of studying the ergodicity and asymptotic stability for various semigroups from dynamic systems and Markov chains. Abundant theories and applications have been established for compact or locally compact state spaces. However, it seems very hard to extend all of them to infinite dimensional or general Polish settings. Actually, the {\em strong Feller} semigroups were the most popular objects in the field of stochastic processes on Banach spaces. Recent years, people have developed many new approaches to more complicated models. For instance, the {\em asymptotic strong Feller} property, as a celebrating breakthrough, was presented by Hairer and Mattingly, which can be applied to deal with the uniqueness of ergodicity for 2D Navier-Stokes equations with degenerate stochastic forcing. Some notable contributions to this subject came from Lasota and Szarek along with their sequential works for {\em equicontinuous} semigroups. Indeed, the equicontinuity is adaptable to many known stochastic partial differential equations at present. However, it seems far from being necessary in the theoretical sense. In this talk, we will give the sharp criterions or equivalent characterizations about the ergodicity and asymptotic stability for {\em Feller} semigroups on Polish spaces with full generality. To this end we will introduce some new notions, especially the {\em eventual continuity} of Feller semigroups, which seems very close to be necessary for the ergodic behavior in some sense and also allows the sensitive dependence on initial data in some extent. |
| 분류기호 (MSC number(s)) |
Primary 60J05, Secondary 37A30 |
| 키워드(Keyword(s)) | ergodicity, asymptotic stability, Feller semigroup, Polish space |
| 강연 형태 (Language of Session (Talk)) |
English |