Topological properties of solution sets for Sobolev-type fractional stochastic differential inclusions with Poisson jumps

2018 ◽  
Vol 99 (8) ◽  
pp. 1373-1401
Author(s):  
Zhi-Han Zhao ◽  
Yong-Kui Chang
Keyword(s):  
Differential Inclusions ◽  
Sobolev Type ◽  
Topological Properties ◽  
Poisson Jumps ◽  
Solution Sets ◽  
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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