Letnbspyt t genbsp0 be the stochastic process defined in

Question

Let {Y(t), t ≥ 0} be the stochastic process defined in Question no. 21.

(a) Calculate the distribution of Y(1 )+ Y(2).

(b) Let T₁ := mm{t > 0:Y(t) = 1}. Calculate the probability density function of the random variable T₁.

Question no. 21

Let {W(t),t ≥ 0} be a Brownian motion with infinitesimal parameters μ = 0 and σ² (> 0). We set