On quantum stochastic differential equations |
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Authors: | J. Martin Lindsay Adam G. Skalski |
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Affiliation: | aDepartment of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK |
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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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Keywords: | Noncommutative probability Quantum stochastic Operator space Stochastic cocycle Lé vy process Coalgebra |
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