Let the process {X(t), t ≥ 0} be defined by X(t) = B 2 (t) − t, where {B(t), t ≥ 0} is a standard Brownian motion. a. What is E[X(t)]? b. Show that {X(t), t ≥ 0} is a martingale. Hint: Start by...

Let the process {X(t), t ≥ 0} be defined by X(t) = B²(t) − t, where {B(t), t ≥ 0} is a standard Brownian motion.

a. What is E[X(t)]?

b. Show that {X(t), t ≥ 0} is a martingale. Hint: Start by computing E[X(t)|B(v), 0 ≤ v ≤ s].