Before revision:  In particular, we show that stickiness is invariant under composition with continuous functions. We also prove a time change result on stickiness. As an application we provide sufficient conditions for continuous semimartingales to be sticky (A counter example show that not all semi-martingales are sticky). As a result, our paper provides an extended class of stochastic processes that are consistent with the no arbitrage property in a market with friction .
After revision:  In particular, we give examples of processes that are consistent with the no arbitrage property in a market with friction .