Mild solutions of evolution quantum stochastic differential equations with nonlocal conditions. (English) Zbl 07271509
Summary: We study existence of a unique mild solution of evolution quantum stochastic differential equations with nonlocal conditions under the strong topology. Using the method of successive approximations, we do not need to transform the nonlocal problem to a fixed point form. The evolution operator \(A\) generates a family of semigroup that are continuous. Nonlocal conditions allow additional measurements of certain phenomena that cannot be captured by the traditional initial conditions. We show that under some given conditions, the mild solution is unique and also stable. The method applied here is much easier when compared with previous methods used in literature.
MSC:
| 47H20 | Semigroups of nonlinear operators |
| 47J25 | Iterative procedures involving nonlinear operators |
| 58D25 | Equations in function spaces; evolution equations |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
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