Consider the stock price process satisfies the following SDE:
$dS_t=\mu_t S_tdt + \sigma S_t dW_t , S_0=s $
and the appreciation rate process $\mu_t$ satisfies the following SDE:
$d\mu_t=(a-\mu_t)dt +dB_t, \mu_0=\mu$
where $W_t, B_t$ are two independent Brownian motions.
Hence, there are two sources of uncertainty in the model, but only one stock available for investment.
My question is: Is this market complete?
And, is it similar to the stock consist of two independent Brownian motions?