Abstract
In a further generalisation of the classical Ito formula, we show that if B = ( A t + A [dagger] t [ratio ] t ∈ [0, 1]) is the Brownian quantum martingale and J = ( J t [ratio ] t ∈ [0, 1]) is a bounded quantum semimartingale, then M = ( B t + J t [ratio ] t ∈ [0, 1]) satisfies the functional quantum Ito formula [ 10 , Section 6] formula here 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.
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