Quantum Independent Increment Processes I

Volume 1865 of the series Lecture Notes in Mathematics pp 181-271


Quantum Stochastic Analysis – an Introduction

  • J. Martin LindsayAffiliated withSchool of Mathematical Sciences, University of Nottingham

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By quantum stochastic analysis is meant the analysis arising from the natural operator filtration of a symmetric Fock space over a Hilbert space of squareintegrable vector-valued functions on the positive half-line. Current texts on quantum stochastics are the monograph [Par], the lecture notes [Mey], the St. Flour lectures [Bia], and the Grenoble lectures [Hud]. Excellent background together with a wealth of examples may be found in these, each of which has its own emphasis. The point of view of these notes is closest to [Bia], as far as the basic construction of quantum stochastic integrals goes. Beyond that, particular emphasis is given to Markovian cocycles.