Stop times in Fock Space Quantum Probability

We review Fock space based quantum probability and in particular the theory of stop times based on it. In the Fock space H = F(L2(R+)), a stop time may be defined as as a positive self-adjoint operator T = ∫ R+ λ dE(λ) whose spectral resolution (E(λ):λ ∈ R+) is adapted to the natural filtration based on the splittings F(L(R)) = F(L([0, λ[)⊗F(L([λ,∞[) Then if K is one of the basic quantum martingales (creation, preservation or annihilation) the corresponding process KT (t) = K(T + t)−K(T ) beginning anew at time T can be defined unambiguosly using functional calculus for the self-adjoint operator T with an operator-valued integrand