For which functions are 𝑓(𝑋_{𝑡})-𝔼𝕗(𝕏_{𝕥}) and 𝕘(𝕏_{𝕥})/𝔼𝕘(𝕏_{𝕥}) martingales?
Publikation: Beitrag in Fachzeitschrift › Forschungsartikel › Beigetragen › Begutachtung
Beitragende
Abstract
Let X = (Xt)t≥0 be a one-dimensional L´evy process such that each Xt has a C1-density w. r. t. Lebesgue measure and certain polynomial or exponen- tial moments. We characterize all polynomially bounded functions f: R → R, and exponentially bounded functions g: R → (0, ∞), such that f (Xt) − Ef (Xt), resp. g(Xt)/Eg(Xt), are martingales.
Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 79-91 |
| Seitenumfang | 13 |
| Fachzeitschrift | Theory of probability and mathematical statistics |
| Jahrgang | 105 |
| Publikationsstatus | Veröffentlicht - Juli 2021 |
| Peer-Review-Status | Ja |
Externe IDs
| Mendeley | 0aae219b-c976-3b34-b284-48009f17abc5 |
|---|---|
| unpaywall | 10.1090/tpms/1157 |
Schlagworte
ASJC Scopus Sachgebiete
Schlagwörter
- Brownian motion, Cauchy functional equation, Choquet–Deny theorem, Convolution equation, Harmonic polynomial, Levy process, Martingale, Polynomial process