Mild Solutions of Quantum Stochastic Differential Equations
Franco Fagnola, Università di Genova
Stephen J. Wills, University of Nottingham
Abstract
We introduce the concept of a mild solution for the
right Hudson-Parthasarathy quantum stochastic differential equation, prove
existence and uniqueness results, and show the correspondence between our
definition and similar ideas in the theory of classical stochastic differential
equations. The conditions that a process must satisfy in order for it to
be a mild solution are shown to be strictly weaker than those for it to
be a strong solution by exhibiting a class of coefficient matrices for
which a mild unitary solution can be found, but for which no strong solution
exists.
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