Stochastic Analysis and Applications

Error Estimates for Discretized Quantum Stochastic Differential Inclusions

E. O. Ayoola

Published Jan 11, 2003• 13 citations

Abstract

This paper is concerned with the error estimates involved in the solution of a discrete approximation of a quantum stochastic differential inclusion (QSDI). Our main results rely on certain properties of the averaged modulus of continuity for multivalued sesquilinear forms associated with QSDI. We obtained results concerning the estimates of the Hausdorff distance between the set of solutions of the QSDI and the set of solutions of its discrete approximation. This extends the results of Dontchev and Farkhi Dontchev, A.L.; Farkhi, E.M. (Error estimates for discre‐ tized differential inclusions. Computing 1989, 41, 349–358) concerning classical differential inclusions to the present noncommutative quantum setting involving inclusions in certain locally convex space.

DOI: 10.1081/sap-120026104

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