On quantum stochastic differential equations

Details On quantum stochastic differential equations On quantum stochastic differential equations

2010-12-30

arxiv.org/abs/1101.0175v1

J. Math. Anal. Appl. 330 (2007) no. 2, 1093-1114

Mathematics

Operator Algebras

20 pages

Scientific paper

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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