For which functions are ๐(๐_{๐ก})-๐ผ๐(๐_{๐ฅ}) and ๐(๐_{๐ฅ})/๐ผ๐(๐_{๐ฅ}) martingales?
Research output: Contribution to journal โบ Research article โบ Contributed โบ peer-review
Contributors
Abstract
Let X = (Xt)tโฅ0 be a one-dimensional Lยดevy 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 โ R, and exponentially bounded functions g: R โ (0, โ), such that f (Xt) โ Ef (Xt), resp. g(Xt)/Eg(Xt), are martingales.
Details
| Original language | English |
|---|---|
| Pages (from-to) | 79-91 |
| Number of pages | 13 |
| Journal | Theory of probability and mathematical statistics |
| Volume | 105 |
| Publication status | Published - Jul 2021 |
| Peer-reviewed | Yes |
External IDs
| Mendeley | 0aae219b-c976-3b34-b284-48009f17abc5 |
|---|---|
| unpaywall | 10.1090/tpms/1157 |
Keywords
ASJC Scopus subject areas
Keywords
- Brownian motion, Cauchy functional equation, ChoquetโDeny theorem, Convolution equation, Harmonic polynomial, Levy process, Martingale, Polynomial process