This paper is concerned with the value function for optimal quantum stochastic control. We established the Lipschitz continuity of the value function, which is inherent from the Lipschitz property of the set-valued map describing the quantum stochastic control. By using a feedback multivalued map, we also prove a characterization of optimal solutions relating to a noncommutative generalization of Mayer problem.

Journal of Mathematical PhysicsFeb 1, 20107 citations

Stochastic Processes in Quantum Systems

C. V. Heer

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Physica A Statistical Mechanics and its Applications

Quantum mappings and the problem of stochasticity in quantum systems

G. P. Berman, G. M. Zaslavsky

Published Mar 1, 1982• 21 citations

Publisher

DOI: 10.1016/0378-4371(82)90081-4

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d

-dimensional system is mapped onto the statics of an associated quantum system and of its classical (

d+1

)-dimensional counterpart. These mappings yield an equality relating the dynamical critical exponent $\ensuremath{\Delta}$ and the static susceptibility exponents of three models.