For which functions are 𝑓(𝑋_{𝑡})-𝔼𝕗(𝕏_{𝕥}) and 𝕘(𝕏_{𝕥})/𝔼𝕘(𝕏_{𝕥}) martingales?

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

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

OriginalspracheEnglisch
Seiten (von - bis)79-91
Seitenumfang13
FachzeitschriftTheory of probability and mathematical statistics
Jahrgang105
PublikationsstatusVeröffentlicht - Juli 2021
Peer-Review-StatusJa

Externe IDs

Mendeley 0aae219b-c976-3b34-b284-48009f17abc5
unpaywall 10.1090/tpms/1157

Schlagworte

Schlagwörter

  • Brownian motion, Cauchy functional equation, Choquet–Deny theorem, Convolution equation, Harmonic polynomial, Levy process, Martingale, Polynomial process

Bibliotheksschlagworte