Variational Stability for Kurzweil Equations associated with Quantum Stochastic Differential Equations
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In this work, The Lyapunov's method is used to establish all kinds of variational stability of solution of quantum stochastic differential equations associated with the Kurzweil equations. The results here generalize analogous results for classical initial value problems to the noncummutative quantum setting involving unbounded linear operators on a Hilbert space. The theory of Kurzweil equations associated with quantum stochastic differential equations provides a basis for subsequent application of the technique of topological dynamics to the study of quantum stochastic differential equations as in the classical cases.
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