Recurrence of the Ornstein–Uhlenbeck process

(i) Determine the recurrence of the d-dimensional Ornstein–Uhlenbeck process, de- fined by the stochastic dynamics dx = −αx dt + dw(t), where α is a positive constant. (ii) Is the Ornstein–Uhlenbeck process recurrent for α positive and negative? (iii) Consider the case that α is a matrix