Quantum Stochastic Calculus as a Unifying Force in Physics and Probability
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A survey is made of the theory of quantum stochastic calculus in Fock space developed by the author and K. R. Parthasarathy, together with some of its applications. Comparison with the classical Ito stochastic calculus of Brownian motion is emphasised, as is the power of the quantum theory to unify aspects of the classical theory of stochastic processes, Boson and Fermion second quantisation and dilations of quantum dynamical semigroups.
KeywordsBrownian Motion Annihilation Operator Infinitesimal Generator Quantum Probability Stochastic Calculus
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- R. L. Hudson, ’Quantum diffusions and cohomology of algebras’, in Proceedings of 1st World Congress of Bernoulli Society, Tashkent 1986.Google Scholar
- R. L. Hudson and M. Evans, ’Multidimensional quantum diffusions’, to appear in Quantum Probability (Oberwolfach) Proceedings 1987, ed. L. Accardi, Springer LNM.Google Scholar
- J.M. Lindsay and K.R. Parthasarathy, ’The passage from random walk to diffusion in quantum probability II’, preprint.Google Scholar
- B. Wiener, J. Mathematics and Physics 2, 131 (1923)Google Scholar