Before revision:  The nature of information flows usually exhibits complex behaviour, however, we succeed in maintaining analytic tractability by introducing what we term the effective and complementary information processes . The effective information captures in a univariate process all information provided by the active sources, and the complementary informationis a function-valued stochastic process which is constant between changes of states. One of the many potential applications is in finance: we associate the signal to a random payoff and price a financial derivative within the modulated information approach.
After revision:  The nature of information flows usually exhibits complex behaviour, however, we succeed in maintaining analytic tractability by introducing what we term the effective and complementary information processes , which dynamically incorporate active and inactive information, respectively. As an application, we price a financial derivative within the modulated information approach.