Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Quantum stochastic operator cocycles via associated semigroups

J. MARTIN LINDSAYa1 and STEPHEN J. WILLSa2

a1 Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF. e-mail: j.m.lindsay@lancaster.ac.uk

a2 School of Mathematical Sciences, University College Cork, Cork, Ireland. e-mail: s.wills@ucc.ie

Abstract

A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their stochastic generators. This leads to new existence results for quantum stochastic differential equations. We also give necessary and sufficient conditions for a cocycle to satisfy such an equation.

(Received December 02 2005)

(Revised July 04 2006)