Let
PT be a stop time in symmetric Fock space over
L2(
R+). We show that to certain unitary operator valued processes
U=(
U(
t),
t{≥}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
PT finite the process (
U(
T+
t),
t{≥}0) is factorised as the product of
U(
T) with a new process
UT=(
UT(
t),
t{≥}0) beginning “after time
T”.
View full abstract