Before revision:  The jump-size distribution is a function of a weighted sum of those information processes that are activated at the jump time. The proposed approach can be applied broadly in signal processing, and an example in Mathematical Finance is provided. We consider a vanilla option and find that its Merton-type price can be expressed by a weighted sum of vanilla prices based on the possible combinations of active information processes at option maturity.
After revision:  The jump-size distribution is a function of 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. It turns out that the price of a vanilla option can be expressed by a weighted sum of vanilla prices based on the possible combinations of active information processes at option maturity.