Summary: Robin Hudson's Pathless Path to Quantum
Department of Probability and Statistics ,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
Robin Hudson's work on quantum central limit theorems, quantum
Brownian motion, quantum stopping times and "formal" quantum
stochastic calculus is reviewed and reappraised.
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" .
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