An extension of stochastic calculus to certain non-Markovian processes

By time changes of Lévy processes we construct two operators on Fock space whose sum is a second quantized operator, and that complement the annihilation and creation operators whose probabilistic interpretations use shifts of trajectories. This results in an analytic construction, for certain nonMarkovian processes, of stochastic calculus including Itô differentials, generators and associated integro-differential equations, without using the notion of filtration.