Before revision:  Starting from positive initial conditions, the state X(k) is governed by a nonnegative constant parameter alpha and a time-varying parameter v(k) with known bounds but otherwise arbitrarily time-varying.
After revision:  Starting from positive initial conditions, the state X(k) is governed by a nonnegative constant parameter alpha and a time-varying parameter v(k) which models asset returns which are within known bounds but otherwise arbitrarily time-varying.