Stopping Unitary Processes in Fock Space
David Applebaum
Let P T be a stop time in symmetric Fock space over L Z (R + ).We show that to certain unitary operator valued processes U=(U(t),t^Q) 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^Q) is factorised as the product of U(T) with a new process U T = (U T (t} , f^O) beginning "after time T".
Publications of the Research Institute for Mathematical Sciences•Oct 31, 1988•3 citations