申論題

≤≤≤≤6. Let N(t) , where 0 ≤ t ≤ T , denote a stochastic process, which satisfies the following conditions:
i. N (0)= 0 .
ii. N (t₂)- N (t₁) is normally distributed with mean 0 and variance t₂ - t₁ , where
0 ≤ t₁ < t₂ ≤ T .

iii. N(t) has independent increments. That is, given

 are mutually independent.
Please answer the following question:

(2). (7%) Please show that the correlation coefficient between N(s) and N(t) is , where 0≤ s < t ≤ T .