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Robin Hudson's Pathless Path to Quantum Stochastic Calculus

Summary: Robin Hudson's Pathless Path to Quantum
Stochastic Calculus
David Applebaum,
Department of Probability and Statistics ,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
Robin Hudson's work on quantum central limit theorems, quantum
Brownian motion, quantum stopping times and "formal" quantum
stochastic calculus is reviewed and reappraised.
1 Introduction
Quantum stochastic calculus was created by Robin Hudson and K.R.
Parthasarathy. The key paper which contained almost all the basic results
was published in 1984 in "Communications in Mathematical Physics" [19].
Here we find, in particular, the construction of quantum stochastic integrals,
quantum It^os formula, the existence and uniqueness of linear quantum sto-
chastic differential equations (QSDEs), necessary and sufficient conditions
for unitarity of solutions and the dilation of quantum dynamical semigroups


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics