Quantum Stochastic Calculus

K. R. Parthasarathy
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K. R. Parthasarathy: Indian Statistical Institute

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1024-1035 from Springer

Abstract: Abstract The basic integrator processes of quantum stochastic calculus, namely, creation, conservation, and annihilation, are introduced in the Hilbert space of square integrable Brownian functionals. Stochastic integrals with respect to these processes and a quantum Itô’s formula are described. As an application two examples of quantum stochastic differential equations are discussed. A continuous time version of Stinespring’s theorem on completely positive maps in C*-algebras is exploited to formulate the notion of a quantum Markov process and indicate how classical Markov processes are woven into the fabric of the Schodinger-Heisenberg dynamics of quantum theory.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_95

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