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arXiv · 1101.0175

On quantum stochastic differential equations

J. Martin Lindsay·Adam G. Skalski
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Abstract

Existence and uniqueness theorems for quantum stochastic differential equations with nontrivial initial conditions are proved for coefficients with completely bounded columns. Applications are given for the case of finite-dimensional initial space or, more generally, for coefficients satisfying a finite localisability condition. Necessary and sufficient conditions are obtained for a conjugate pair of quantum stochastic cocycles on a finite-dimensional operator space to strongly satisfy such a quantum stochastic differential equation. This gives an alternative approach to quantum stochastic convolution cocycles on a coalgebra.

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J. Martin Lindsay, Adam G. Skalski. 2010-12-30. On quantum stochastic differential equations. https://arxiv.org/abs/1101.0175

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