Ornstein-Uhlenbeck Process

Let $(W_t)_{t \geq 0}$ be a standard Brownian motion. Consider the process $X_t$ solution to the following stochastic differential equation:

dX_t = -aX_t \, dt + \sigma \, dW_t, \quad X_0 = x_0, \quad a > 0,\; \sigma > 0.

Question: Determine the distribution of $X_t$ .

Answer