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Quantum stochastic calculus with maximal operator domains.

Research output: Contribution to journalJournal articlepeer-review

<mark>Journal publication date</mark>1/01/2004
<mark>Journal</mark>Annals of Probability
Issue number1a
Number of pages42
Pages (from-to)488-529
Publication StatusPublished
<mark>Original language</mark>English


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 time filtration of Fock space, together with sections of the adapted gradient operator. Free from exponential vector domains, our stochastic integrals may be satisfactorily composed yielding quantum Itô formulas for operator products as sums of stochastic integrals. The calculus has seen two reformulations since its discovery—one closely related to classical Itô calculus; the other to noncausal stochastic analysis and Malliavin calculus. Our theory extends both of these approaches and may be viewed as a synthesis of the two. The main application given here is existence and uniqueness for the Attal–Meyer equations for implicit definition of quantum stochastic integrals.

Bibliographic note

RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics