Existence and Uniqueness of Solutions of a Class of Quantum Stochastic Evolution Equations

We study the existence and uniqueness of solutions of a class of Quantum Stochastic Evolution Equations (QSEEs) dened on a locally convex space whose topology is generated by a family of semi- norms dened via the norm of the range space of the operator processes. These solutions are called strong solutions in comparison with the so- lutions of similar equations dened on the space of operator processes where the topology is generated by the family of seminorms dened via the inner product of the range space. The evolution operator gen- erates a bounded semigroup. We show that under some more general conditions, the unique solution is stable. These results extend some ex- isting results in the literature concerning strong solutions of quantum stochastic differential equations.