9.8 Let the process fXt; t $ 0g be defined by Xt 5 B2t 2 t, where

9.8 Let the process fXðtÞ; t $ 0g be defined by XðtÞ 5 B2ðtÞ 2 t, where fBðtÞ; t $ 0g is a standard Brownian motion.

a. What is E½XðtÞ?

b. Show that fXðtÞ; t $ 0g is a martingale. Hint: Start by computing E½XðtÞjBðvÞ; 0 # v # t.