The Stability of some stochastic processes

Abstract: We formulate and prove a new criterion for stability of e-processes. It says that any e-process which is averagely bounded and concentrating is asymptotically stable. In the second part, we show how this general result applies to some shell models (the Goy and the Sabra model). Indeed, we manage to prove that the processes corresponding to these models satisfy the e-process property. They are also averagely bounded and concentrating. Consequently, their stability follows.