Open AccessNon-extremal martingale with Brownian filtration
Author(s) -
Samia Sakrani
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.45542
Subject(s) - martingale (probability theory) , mathematics , brownian motion , filtration (mathematics) , martingale representation theorem , local martingale , pure mathematics , diffusion process , geometric brownian motion , statistics , computer science , knowledge management , innovation diffusion
Let (B_{t})_{t≥0} be the filtration of a Brownian motion (B_{t})_{t≥0} on (Ω,B,P). An example is given of an non-extremal martingale which generates the filtration (B_{t})_{t≥0}. We also discuss a property of pure martingales, we show here that it is a property of a filtration rather than a martingale.