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

Sheila A. Bishop, E.O. Ayoola

Abstract


We study the properties of the existence and uniqueness of solu-tions of a class of evolution quantum stochastic differential equations(QSDEs) dened on a locally convex space whose topology is gen-erated by a family of seminorms dened via the norm of the rangespace of the operator processes. These solutions are called strong solutions in comparison with the solutions of similar equations denedon the space of operator processes where the topology is generated bythe family of seminorms dened via the inner product of the rangespace. The evolution operator generates a bounded semigroup. Weshow that under some more general conditions, the unique solutionis stable. These results extend some existing results in the literatureconcerning strong solutions of quantum stochastic differential equa-tions.

Keywords


Strong solutions; Stability; Bounded semigroup; General Lipschitz condition

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