In this paper, we introduce a non-commutative space of stochastic distributions, which contains the non-commutative white noise space, and forms, together with a natural multiplication, a topological algebra. Special inequalities which hold in this space allow to characterize its invertible elements and to develop an appropriate framework of non-commutative stochastic linear systems.
D. Alpay and G. Salomon. Non-commutative stochastic distributions and applications to linear systems theory. Stochastic Processes and Applications, vol. 123 (2013), pp. 2303-2322.
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