1. Prove that for any positve h the stochastic process {V(t), t ≥ 0} defined by V(t) = B(t + h) − B(t) is weakly stationary. 2. Prove that the stochastic process {X(t), t ≥ 0} with X(t) = S 3 (t) − 3t...

1. Prove that for any positve h the stochastic process {V(t), t ≥ 0} defined by

V(t) = B(t + h) − B(t)

is weakly stationary.

2. Prove that the stochastic process {X(t), t ≥ 0} with X(t) = S³(t) − 3t S(t) is a continuous-time martingale, i.e show that