Abstract
A class of non-Markovian stochastic processes is defined; it generalizes several anterior models, and allows a trajectorial description of collisions in dense fluids when the system loses all memory at each collision. The abstract formalism is studied here: an integral evolution equation is derived, as well as an integrodifferential equation that generalizes the master equation; some asymptotic properties of these processes are established. Applications to specific models will be treated in other articles.
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