An Introduction to Quantum Stochastic Calculus aims to deepen our
understanding of the dynamics of systems subject to the laws of chance
both from the classical and the quantum points of view and stimulate
further research in their unification. This is probably the first
systematic attempt to weave classical probability theory into the
quantum framework and provides a wealth of interesting features:
The origin of Ito's correction formulae for Brownian motion and the
Poisson process can be traced to commutation relations or, equivalently,
the uncertainty principle.
Quantum stochastic integration enables the possibility of seeing new
relationships between fermion and boson fields.
Many quantum dynamical semigroups as well as classical Markov semigroups
are realised through unitary operator evolutions.
The text is almost self-contained and requires only an elementary
knowledge of operator theory and probability theory at the graduate
level.
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This is an excellent volume which will be a valuable companion both to
those who are already active in the field and those who are new to it.
Furthermore there are a large number of stimulating exercises scattered
through the text which will be invaluable to students.
(Mathematical Reviews)
This monograph gives a systematic and self-contained introduction to
the Fock space quantum stochastic calculus in its basic form (...) by
making emphasis on the mathematical aspects of quantum formalism and its
connections with classical probability and by extensive presentation of
carefully selected functional analytic material. This makes the book
very convenient for a reader with the probability-theoretic orientation,
wishing to make acquaintance with wonders of the noncommutative
probability, and, more specifcally, for a mathematics student studying
this field.
(Zentralblatt MATH)
*Elegantly written, with obvious appreciation for fine points of higher
mathematics (...) most notable is [the] author's effort to weave
classical probability theory into [a] quantum framework.
*(The American Mathematical Monthly)
