# Journal of Operator Theory

Volume 36, Issue 2, Fall 1996 pp. 295-316.

Infinite series of quantum spectral stochastic integrals**Authors**: David Applebaum (1) and Martin Brooks (2)

**Author institution:**(1) Department of Mathematics, Statistics and Operational Research, The Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, ENGLAND

(2) Department of Mathematics, Statistics and Operational Research, The Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, ENGLAND

**Summary:**We obtain sufficient conditions for the convergence of infinite series of quantum spectral stochastic integrals. The resulting operator-valued processes are used to drive quantum stochastic integro-differential equations. Unitary solutions of these equations implement quantum stochastic flows and give rise to a new representation for the generators of a class of completely positive semigroups. As an application, we are able to construct a class of flows on algebras of operators which are driven by multidimensional LÃ©vy processes.

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