Weak Compactness of Solution Sets to Stochastic Differential Inclusions with Non-Convex Right-Hand Sides

2005 ◽  
Vol 23 (5) ◽  
pp. 871-901 ◽  
Author(s):  
Michał Kisielewicz
Keyword(s):  
Differential Inclusions ◽  
Weak Compactness ◽  
Solution Sets ◽  
Right Hand ◽  
Stochastic Differential Inclusions

Further results on the arcwise connectedness of solution sets of discontinuous quantum stochastic differential inclusions

2020 ◽  
Vol 23 (03) ◽  
pp. 2050022
Author(s):  
D. A. Dikko
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Stochastic Calculus ◽  
Matrix Elements ◽  
Quantum Stochastic Calculus ◽  
Solution Sets ◽  
Stochastic Differential Inclusions ◽  
The Matrix ◽  
Arcwise Connected ◽  
Stochastic Differential Inclusion

In the framework of the Hudson–Parthasarathy quantum stochastic calculus, we employ a recent generalization of the Michael selection results in the present noncommutative settings to prove that the function space of the matrix elements of solutions to discontinuous quantum stochastic differential inclusion (DQSDI) is arcwise connected.

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