Quantum Probability for Probabilists
Meyer, Paul-André.
Quantum Probability for Probabilists [electronic resource] / by Paul-André Meyer. - XII, 316 p. online resource. - Lecture Notes in Mathematics, 1538 0075-8434 ; . - Lecture Notes in Mathematics, 1538 .
Non-commutative probability -- Spin -- The harmonic oscillator -- Fock space (1) -- Fock space (2): Multiple fock spaces -- Stochastic calculus in Fock space -- Independent increments.
In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide an introduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of stochastic calculus for physicists familiar with Fock space analysis. For this second edition, the author has added about 30 pages of new material, mostly on quantum stochastic integrals.
9783540369592
10.1007/BFb0084701 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
QA273.A1-274.9 QA274-274.9
519.2
Quantum Probability for Probabilists [electronic resource] / by Paul-André Meyer. - XII, 316 p. online resource. - Lecture Notes in Mathematics, 1538 0075-8434 ; . - Lecture Notes in Mathematics, 1538 .
Non-commutative probability -- Spin -- The harmonic oscillator -- Fock space (1) -- Fock space (2): Multiple fock spaces -- Stochastic calculus in Fock space -- Independent increments.
In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide an introduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, provide a means of access to the methods of stochastic calculus for physicists familiar with Fock space analysis. For this second edition, the author has added about 30 pages of new material, mostly on quantum stochastic integrals.
9783540369592
10.1007/BFb0084701 doi
Distribution (Probability theory.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
QA273.A1-274.9 QA274-274.9
519.2