Quantum Probability for ProbabilistsIn 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. |
Contents
Chapter I | 1 |
Chapter II Spin | 13 |
Chapter III | 43 |
Chapter IV | 57 |
Chapter V | 103 |
122 | 122 |
Chapter VI | 125 |
132 | 132 |
Chapter VII | 195 |
204 | 204 |
Appendix 1 | 209 |
Appendix 2 | 218 |
Appendix 3 | 231 |
Appendix 4 | 234 |
Appendix 5 | 264 |
Appendix 6 | 286 |
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Common terms and phrases
adjoint annihilation operators anticommutation antisymmetric arbitrary assume basis Bernoulli bilinear bounded operators Brownian motion C*-algebra chaos Chapter classical probability coefficients commutative complex condition consider construction continuous convergence corresponding creation and annihilation define denote discrete elements exponential domain exponential vectors Fock space Gaussian given Hilbert space homomorphism initial space isomorphism kernels L2 space linear functional Maassen mapping Markov martingale matrix measure multiple Fock space multiplication operator Neumann algebra non-commutative norm normal notation number operator Parthasarathy Poisson positive probabilistic interpretation proof prove random variables relation representation result satisfies scalar product selfadjoint semigroup semimartingales simple Fock space space H spectral spin stochastic calculus stochastic integral subsection subspace symmetric tensor product theorem theory topology toy Fock space uniqueness unitary group vacuum values von Neumann algebra Weyl operators Wick product Wiener product
References to this book
Combinatorial Theory of the Free Product with Amalgamation and ..., Issue 627 Roland Speicher No preview available - 1998 |
Integral Transformations and Anticipative Calculus for ..., Volume 825 Yaozhong Hu No preview available - 2005 |