Akinwumi Titilayo O and Ayoola Ezekiel O. Viable Solutions of Lipschitzian Quantum Stochastic Differential Equations. Neural Parallel and Scientific Computations 29 (2021), No. 1,  1-19

https://doi.org/10.46719/NPSC20212911

ABSTRACT.
We establish the existence of viable solutions of quantum stochastic differential equations (QSDE) within the framework of Hudson and Parthasarathy formulation of quantum stochastic calculus. The main results are established for QSDE whose coefficients are Lipschitzian and quasi-compact. This work extends the Nagumo viability results for classical differential equations on finite dimensional Euclidean spaces. Viable solutions of QSDE in the present formulation take values in some closed subsets of the infinite dimensional locally convex spaces of non-commutative stochastic processes.

AMS (MOS) Subject Classification. (2020) 60H10, 60H20, 81S25
Keywords and Phrases. Lipschitzian, Quasi-compact, Fock Spaces, Tangent cones