scholarly journals Convex combinations of low eigenvalues, Fraenkel asymmetries and attainable sets

2017 ◽  
Vol 23 (3) ◽  
pp. 869-887 ◽  
Author(s):  
Dario Mazzoleni ◽  
Davide Zucco
Keyword(s):  
Attainable Sets

Stochastic inclusions and set-valued stochastic equations driven by a two-parameter Wiener process

2018 ◽  
Vol 18 (06) ◽  
pp. 1850047 ◽  
Author(s):  
Mariusz Michta ◽  
Kamil Łukasz Świa̧tek
Keyword(s):  
Wiener Process ◽  
Stochastic Equation ◽  
Stochastic Equations ◽  
Continuous Selection ◽  
Attainable Sets ◽  
Multivalued Solution ◽  
Stochastic Differential Inclusions ◽  
Multivalued Solutions ◽  
Two Parameter ◽  
Selection Of

In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.

Limit Behavior of Attainable Sets of Linear Systems

Computing ◽  
2005 ◽  
Vol 75 (1) ◽  
pp. 99-107 ◽  
Author(s):  
A. I. Ovseevich
Keyword(s):  
Linear Systems ◽  
Limit Behavior ◽  
Attainable Sets

scholarly journals Attainable sets and one-parameter semigroups of sets

1991 ◽  
Vol 33 (2) ◽  
pp. 187-201 ◽  
Author(s):  
I. Chon ◽  
J. D. Lawson
Keyword(s):  
Control Systems ◽  
Lie Groups ◽  
Vector Fields ◽  
Geometric Control ◽  
Lie Theory ◽  
Attainable Sets ◽  
Widespread Application ◽  
Close Relationship ◽  
Basic Facts ◽  
Systems On Lie Groups

The methods of Lie theory have found widespread application in the study of the Lie algebras of vector fields on manifolds that arise naturally in geometric control theory (for some such applications, see [1]). Control systems on Lie groups themselves also have received considerable attention (see, for example, [9]). After reviewing basic facts about control systems on Lie groups, we derive the close relationship between attainable sets and Rådström's theory [12] of one-parameter semigroups of sets (Section 2). These ideas are then linked to the recently emerging Lie theory of semigroups [5]. The authors are indebted to the referee for pointing out some of the pertinent literature and analogous results from the area of geometric control.

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