For which functions are f (Xt) − Ef (Xt) and g(Xt)/Eg(Xt) martingales?
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
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
| Original language | English |
|---|---|
| Pages (from-to) | 79-91 |
| Number of pages | 13 |
| Journal | Theory of probability and mathematical statistics |
| Volume | 105 |
| Publication status | Published - 2021 |
| Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- Brownian motion, Cauchy functional equation, Choquet–Deny theorem, Convolution equation, Harmonic polynomial, Levy process, Martingale, Polynomial process