The maximal process of nonlinear shot noise

In the nonlinear shot noise system-model shots’ statistics are governed by general Poisson processes, and shots’ decay-dynamics are governed by general nonlinear differential equations. In this research we consider a nonlinear shot noise system and explore the process tracking, along time, the system’s maximal shot magnitude. This ‘maximal process’ is a stationary Markov process following a decay–surge evolution; it is highly robust, and it is capable of displaying both a wide spectrum of statistical behaviors and a rich variety of random decay–surge sample-path trajectories. A comprehensive analysis of the maximal process is conducted, including its Markovian structure, its decay–surge structure, and its correlation structure. All results are obtained analytically and in closed-form.