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.

scholarly journals Existence of solutions of functional stochastic differential inclusions

2002 ◽  
Vol 33 (1) ◽  
pp. 25-34 ◽  
Author(s):  
P. Balasubramaniam
Keyword(s):  
Fixed Point ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Analysis Approach ◽  
Point Analysis ◽  
Stochastic Differential Inclusions ◽  
Stochastic Differential Inclusion

In this paper, we prove the existence of solutions for functional stochastic differential inclusion via a fixed point analysis approach.

scholarly journals Continuous Interpolation of Solution Sets of Lipschitzian Quantum Stochastic Differential Inclusions

2007 ◽  
Vol 2007 ◽  
pp. 1-12
Author(s):  
E. O. Ayoola ◽  
John O. Adeyeye
Keyword(s):  
Continuous Selection ◽  
Stochastic Differential Inclusions ◽  
The Matrix ◽  
Finite Set ◽  
The Difference ◽  
Continuous Interpolation ◽  
The Given ◽  
Complex Valued ◽  
Locally Convex ◽  
Stochastic Differential Inclusion

Given any finite set of trajectories of a Lipschitzian quantum stochastic differential inclusion (QSDI), there exists a continuous selection from the complex-valued multifunction associated with the solution set of the inclusion, interpolating the matrix elements of the given trajectories. Furthermore, the difference of any two of such solutions is bounded in the seminorm of the locally convex space of solutions.

scholarly journals Regular and singular perturbations of upper semicontinuous differential inclusion

1997 ◽  
Vol 20 (4) ◽  
pp. 699-706 ◽  
Author(s):  
Tzanko Donchev ◽  
Vasil Angelov
Keyword(s):  
Differential Inclusion ◽  
Singular Perturbations ◽  
Differential Inclusions ◽  
Existence Result ◽  
Lower Semicontinuous ◽  
Solution Set ◽  
Singularly Perturbed ◽  
Solution Sets ◽  
Upper Semicontinuous ◽  
Continuity Properties

In the paper we study the continuity properties of the solution set of upper semicontinuous differential inclusions in both regularly and singularly perturbed case. Using a kind of dissipative type of conditions introduced in [1] we obtain lower semicontinuous dependence of the solution sets. Moreover new existence result for lower semicontinuous differential inclusions is proved.

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