12,000

We have over 12,000 students, from over 100 countries, within one of the safest campuses in the UK

93%

93% of Lancaster students go into work or further study within six months of graduating

Home > Research > Publications & Outputs > Quantum stochastic calculus with maximal operat...
View graph of relations

« Back

Quantum stochastic calculus with maximal operator domains.

Research output: Contribution to journalJournal article

Published

Journal publication date1/01/2004
JournalAnnals of Probability
Journal number1a
Volume32
Number of pages42
Pages488-529
Original languageEnglish

Abstract

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