We study an Adaptive Window Protocol (AWP) with a general increase and decrease profiles in the presence of window dependent random losses. We derive a steady-state Kolmogorov equation and then obtain its solution in analytic form. We then derive from the model some monotonicity properties of the window size process. These monotonicity properties are then used to obtain a necessary and sufficient condition for stability of the window evolution process. Finally, we apply the general results to particular TCP versions such as New Reno TCP, Scalable TCP and HighSpeed TCP.