Exercise 13.5 For two standard Brownian motions {z1(t)} and {z2(t)}, suppose that the correlation coefficient between z1(t)

Exercise 13.5 For two standard Brownian motions {z1(t)} and {z2(t)}, suppose that the correlation coefficient between Δz1(t) and Δz2(t) is ρ. Let

Δz(t) be the increment of another standard Brownian motion {z(t)}, independent of Δz1(t). Then, from Proposition 11.4, we have Δz2(t) d=

ρΔz1(t)+ √

1 − ρ2Δz(t), where d=

stands for equality in law. Using this and (13.16), prove that (13.17) holds.