Stopping unitary processes in Fock space (Q1112456)

Let \(P^ T\) be a stop time in symmetric Fock space over \(L^ 2({\mathbb{R}}^+)\). We show that to certain unitary operator valued processes \(U=(U(t),t\geq 0)\) which satisfy a stochastic differential equation driven by ``non-commutative noise'' in Fock space tensored with an ``initial'' Hilbert space, we can associate a stopped operator U(t). We use these operators to prove a ``stopped cocycle relation'' whereby for \(P^ T\) finite the process \((U(T+t)\), \(t\geq 0)\) is factorized as the product of U(T) with a new process \(U^ T=(U^ T(t)\), \(t\geq 0)\) beginning ``after time T''.