This preview shows page 1. Sign up to view the full content.
Unformatted text preview: X with ﬁnite expectation, it holds that E { XY G} = Y E { X G} . 5) Let { B t : t ≥ } be a Brownian motion, and {F B t } t ≥ be the ﬁltration generated by B . Using the deﬁnition of a Brownian motion to verify that B is indeed an {F B t }martingale. 6) Suppose that { B t : t ≥ } is a standard Brownian motion. Show that for any constant c > 0, the scaled process W t := √ cB t/c , t ≥ 0 is also a standard Brownian motion. 7) Let σ , τ be two stopping times, show that both σ ∧ τ and σ ∨ τ are also stopping times. 1...
View
Full
Document
This note was uploaded on 10/08/2010 for the course MA 503 taught by Professor Majin during the Fall '09 term at USC.
 Fall '09
 MAJIN
 Variance

Click to edit the document details