The Ito Formula for Perturbed Brownian Martingales
G. F. Vincent-Smith
In a further generalisation of the classical Ito formula, we show that if B = ( A t + A t † : t ∈ ] 0 , 1 [ ) is the Brownian quantum martingale and J = (Jt: t ∈ [0, 1]) is a bounded quantum semimartingale, then M = (Bt Jt: t ∈ [0, 1]) satisfies the functional quantum Ito formula [10, Section 6] [formula] The proof, which relies on the classical theory of unbounded self-adjoint operators, may be adapted to the case where B is replaced by a classical Brownian martingale. 2000 Mathematics Subject Classification 81S25, 60J65, 47D03.
Bulletin of the London Mathematical Society•Nov 1, 2000•3 citations