Quantum stochastic calculus and quantum nonlinear filtering
چکیده
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A ?algebraic inde nite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability conditions in an in nitely dimensional nuclear space. The class of nondemolition output Q
Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the t
Quantum stochastic calculus is applied to the proof of Skorokhod and Weitzenböck type identities for functionals of a Lie group-valued Brownian motion. In contrast to the case of Rd-valued paths, the computations use all three basic quantum stochastic differentials.
Generalising the previous Fock case, we show that in an extremal universally invariant representation of the canonical commutation relations, a second quantised double product of infinitesimal rotations is a stochastic double product in the corresponding non-Fock quantum stochast
We show that iterated stochastic integrals can be described equivalently either by the conventional forward adapted, or by backward adapted quantum stochastic calculus. By using this equivalence we establish two properties of triangular (causal) and rectangular double quantum sto
Detereministic classical dynamics, reversible quantum dynamics in the Schrr odinger-Heinsenberg pictures and irreversible dynamics of diiusion processes driven by Brownian motion admitìnnnitesimal' or`diierential' descriptions which can be expressed in terms of derivations of * a