The Experts below are selected from a list of 297 Experts worldwide ranked by ideXlab platform
Jinghai Shao - One of the best experts on this subject based on the ideXlab platform.
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Criteria for transience and recurrence of regime-switching diffusion processes *
Electronic Journal of Probability, 2015Co-Authors: Jinghai ShaoAbstract:We provide some criteria for recurrence of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a finite Space or in an infinite Countable Space are all studied in this work. Especially, we put forward a finite partition method to deal with switching processes in an infinite Countable Space. As an application, we study the recurrence of regime-switching Ornstein-Uhlenbeck process, and provide a necessary and sufficient condition for a kind of nonlinear regime-switching diffusion processes.
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criteria for transience and recurrence of regime switching diffusion processes
Electronic Journal of Probability, 2015Co-Authors: Jinghai ShaoAbstract:We provide some criteria for recurrence of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a finite Space or in an infinite Countable Space are all studied in this work. Especially, we put forward a finite partition method to deal with switching processes in an infinite Countable Space. As an application, we study the recurrence of regime-switching Ornstein-Uhlenbeck process, and provide a necessary and sufficient condition for a kind of nonlinear regime-switching diffusion processes.
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Criteria for transience and recurrence of regime-switching diffusion processes *
Electronic Journal of Probability, 2015Co-Authors: Jinghai ShaoAbstract:We provide some on-off type criteria for recurrence of regime-switching diffusion processes using the theory of M-matrix, the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a finite Space and an infinite Countable Space are both studied. Especially, we put forward a finite partition method to deal with switching process in an infinite Countable Space. As an application, we study the recurrence of regime-switching Ornstein-Uhlenbeck process, and provide an on-off type criterion for a kind of nonlinear regime-switching diffusion processes.
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criteria for transience and recurrence of regime switching diffusion processes
arXiv: Probability, 2014Co-Authors: Jinghai ShaoAbstract:We provide some on-off type criteria for recurrence and transience of regime-switching diffusion processes using the theory of M-matrix and the Perron-Frobenius theorem. State-independent and state-dependent regime-switching diffusion processes in a finite Space and a Countable Space are both studied. We put forward a finite partition method to deal with switching process in a Countable Space. As an application, we improve the known criteria for recurrence of linear regime-switching diffusion processes, and provide an on-off type criterion for a kind of nonlinear regime-switching diffusion processes.
Monica Patriche - One of the best experts on this subject based on the ideXlab platform.
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Fuzzy games with a Countable Space of actions and applications to systems of generalized quasi-variational inequalities
Fixed Point Theory and Applications, 2014Co-Authors: Monica PatricheAbstract:We introduce an abstract fuzzy economy (generalized fuzzy game) model with a Countable Space of actions, and we study the existence of fuzzy equilibrium. As application, we prove the existence of solutions for the systems of generalized quasi-variational inequalities with random fuzzy mappings, defined in this paper. Our results bring novelty to the current literature by considering random fuzzy mappings whose values are fuzzy sets over complete Countable metric Spaces.
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Fuzzy games with a Countable Space of actions and applications to systems of generalized quasi-variational inequalities
arXiv: Optimization and Control, 2013Co-Authors: Monica PatricheAbstract:In this paper, we introduce an abstract fuzzy economy (generalized fuzzy game) model with a Countable Space of actions and we study the existence of the fuzzy equilibrium. As applications, two types of results are obtained. The first ones concern the existence of the solutions for systems of generalized quasi-variational inequalities with random fuzzy mappings which we define. The last ones are new random fixed point theorems for correspondences with values in complete Countable metric Spaces.
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existence of equilibrium for an abstract economy with private information and a Countable Space of actions
arXiv: Optimization and Control, 2013Co-Authors: Monica PatricheAbstract:We define the model of an abstract economy with private information and a Countable set of actions. We generalize the H. Yu and Z. Zhang's model (2007), considering that each agent is characterised by a preference correspondence instead of having an utility function. We establish two different equilibrium existence results.
Vladimir V. Tkachuk - One of the best experts on this subject based on the ideXlab platform.
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Some applications of discrete selectivity and Banakh property in function Spaces
European Journal of Mathematics, 2019Co-Authors: Vladimir V. TkachukAbstract:We establish that an unCountable Space X must be essentially unCountable whenever its extent and tightness are Countable. As a consequence, the equality $$\mathrm{ext}(X)= t(X)=\omega $$ ext ( X ) = t ( X ) = ω implies that the Space $$C_{p}(X, [0,1])$$ C p ( X , [ 0 , 1 ] ) is discretely selective. If X is a metrizable Space, then $$C_{p}(X, [0,1])$$ C p ( X , [ 0 , 1 ] ) has the Banakh property if and only if so does $$C_{p}(Y, [0,1])$$ C p ( Y , [ 0 , 1 ] ) for some closed separable $$Y\subset X$$ Y ⊂ X . We apply the above results to show that, for a metrizable X , the Space $$C_{p}(X, [0,1])$$ C p ( X , [ 0 , 1 ] ) is strongly dominated by a second Countable Space if and only if X is homeomorphic to $$D\,{\oplus }\, M$$ D ⊕ M where D is a discrete Space and M is Countable. For a metrizable Space X , we also prove that $$C_{p}(X,[0,1])$$ C p ( X , [ 0 , 1 ] ) has the Lindelöf $$\Sigma $$ Σ -property if and only if the set of non-isolated points of X is second Countable. Our results solve several open questions.
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If Cp(X) is strongly dominated by a second Countable Space, then X is Countable
Journal of Mathematical Analysis and Applications, 2017Co-Authors: D. Guerrero Sánchez, Vladimir V. TkachukAbstract:Abstract We establish that a Tychonoff Space X is Countable if and only if C p ( X ) is strongly dominated by a second Countable Space. The same is true for a compact Space K such that C p ( K , [ 0 , 1 ] ) is strongly dominated by a second Countable Space. We also prove that strong domination by a second Countable Space of the complement of the diagonal of a Tychonoff Space X implies that X is an ℵ 0 -Space. Our results solve several published open questions.
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Strong domination by Countable and second Countable Spaces
Topology and its Applications, 2017Co-Authors: Vladimir V. TkachukAbstract:Abstract We show that, for a Lindelof Σ-Space X, if C p ( X , [ 0 , 1 ] ) is strongly dominated by a second Countable Space, then X is Countable. Under Martin's Axiom we prove that there exists a Countable Space Z that strongly dominates the complement of the diagonal of any first Countable compact Space. In particular, strong domination by a Countable Space of the complement of the diagonal of a compact Space X need not imply metrizability of X. It turns out that the same Countable Space Z strongly dominates C p ( X ) for an unCountable Space X. Our results solve several published open problems.
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Calibers, $$\omega $$ -continuous maps and function Spaces
Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A. Matematicas, 2014Co-Authors: Oleg G. Okunev, Vladimir V. TkachukAbstract:The operation of extending functions from $$\scriptstyle X$$ to $$\scriptstyle \upsilon X$$ is $$\scriptstyle \omega $$ -continuous, so it is natural to study $$\scriptstyle \omega $$ -continuous maps systematically if we want to find out which properties of $$\scriptstyle C_p(X)$$ “lift” to $$\scriptstyle C_p(\upsilon X)$$ . We study the properties preserved by $$\scriptstyle \omega $$ -continuous maps and bijections both in general Spaces and in $$\scriptstyle C_p(X)$$ . We show that $$\scriptstyle \omega $$ -continuous maps preserve primary $$\scriptstyle \Sigma $$ -property as well as Countable compactness. On the other hand, existence of an $$\scriptstyle \omega $$ -continuous injection of a Space $$\scriptstyle X$$ to a second Countable Space does not imply $$\scriptstyle G_\delta $$ -diagonal in $$\scriptstyle X$$ ; however, existence of such an injection for a countably compact $$\scriptstyle X$$ implies metrizability of $$\scriptstyle X$$ . We also establish that $$\scriptstyle \omega $$ -continuous injections can destroy caliber $$\scriptstyle \omega _1$$ in pseudocompact Spaces. In the context of relating the properties of $$\scriptstyle C_p(X)$$ and $$\scriptstyle C_p(\upsilon X)$$ , a countably compact subSpace of $$\scriptstyle C_p(X)$$ remains countably compact in the topology of $$\scriptstyle C_p(\upsilon X)$$ ; however, compactness, pseudocompactness, Lindelöf property and Lindelöf $$\scriptstyle \Sigma $$ -property can be destroyed by strengthening the topology of $$\scriptstyle C_p(X)$$ to obtain the Space $$\scriptstyle C_p(\upsilon X)$$ . We show that Lindelöf $$\scriptstyle \Sigma $$ -property of $$\scriptstyle C_p(X)$$ together with $$\scriptstyle \omega _1$$ being a caliber of $$\scriptstyle C_p(X)$$ implies that $$\scriptstyle X$$ is cosmic.
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Calibers, \omega -continuous maps and function Spaces
Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A. Matematicas, 2012Co-Authors: Oleg Okunev, Vladimir V. TkachukAbstract:The operation of extending functions from \(\scriptstyle X\) to \(\scriptstyle \upsilon X\) is \(\scriptstyle \omega \)-continuous, so it is natural to study \(\scriptstyle \omega \)-continuous maps systematically if we want to find out which properties of \(\scriptstyle C_p(X)\) “lift” to \(\scriptstyle C_p(\upsilon X)\). We study the properties preserved by \(\scriptstyle \omega \)-continuous maps and bijections both in general Spaces and in \(\scriptstyle C_p(X)\). We show that \(\scriptstyle \omega \)-continuous maps preserve primary \(\scriptstyle \Sigma \)-property as well as Countable compactness. On the other hand, existence of an \(\scriptstyle \omega \)-continuous injection of a Space \(\scriptstyle X\) to a second Countable Space does not imply \(\scriptstyle G_\delta \)-diagonal in \(\scriptstyle X\); however, existence of such an injection for a countably compact \(\scriptstyle X\) implies metrizability of \(\scriptstyle X\). We also establish that \(\scriptstyle \omega \)-continuous injections can destroy caliber \(\scriptstyle \omega _1\) in pseudocompact Spaces. In the context of relating the properties of \(\scriptstyle C_p(X)\) and \(\scriptstyle C_p(\upsilon X)\), a countably compact subSpace of \(\scriptstyle C_p(X)\) remains countably compact in the topology of \(\scriptstyle C_p(\upsilon X)\); however, compactness, pseudocompactness, Lindelof property and Lindelof \(\scriptstyle \Sigma \)-property can be destroyed by strengthening the topology of \(\scriptstyle C_p(X)\) to obtain the Space \(\scriptstyle C_p(\upsilon X)\). We show that Lindelof\(\scriptstyle \Sigma \)-property of \(\scriptstyle C_p(X)\) together with \(\scriptstyle \omega _1\) being a caliber of \(\scriptstyle C_p(X)\) implies that \(\scriptstyle X\) is cosmic.
João Correia-da-silva - One of the best experts on this subject based on the ideXlab platform.
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Agreeing to disagree in a Countable Space of equiprobable states
Economic Theory, 2010Co-Authors: João Correia-da-silvaAbstract:An example is given in which agents agree to disagree, showing that Aumann’s (1976) Agreement Theorem does not extend to a Countable Space of equiprobable states of nature. Even in this unorthodox setting, if the sets of the information partitions are intervals, an agreement theorem holds. A result that describes the margin for disagreement is also obtained.
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Agreeing to disagree in a Countable Space of equiprobable states of nature
Economic Theory, 2009Co-Authors: João Correia-da-silvaAbstract:Agreeing to disagree, Interactive epistemology, Theory of probability, Countable additivity, Bounded rationality, C70, D82, D84,
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Agreeing to disagree in a Countable Space of equiprobable states of nature
Economic Theory, 2009Co-Authors: João Correia-da-silvaAbstract:An example is given in which agents agree to disagree in a Countable Space of equiprobable states of nature. Even in this unorthodox setting, if the sets of the information partitions are intervals, an agreement theorem holds. A result that describes the margin for disagreement is also obtained.
Yan-kui Song - One of the best experts on this subject based on the ideXlab platform.
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Remarks on absolutely star Countable Spaces
Open Mathematics, 2013Co-Authors: Yan-kui SongAbstract:We prove the following statements: (1) every Tychonoff linked-Lindelof (centered-Lindelof, star Countable) Space can be represented as a closed subSpace in a Tychonoff pseudocompact absolutely star Countable Space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelof Space can be represented as a closed Gδ-subSpace in a Hausdorff (regular, Tychonoff) absolutely star Countable Space; (3) there exists a pseudocompact absolutely star Countable Tychonoff Space having a regular closed subSpace which is not star Countable (hence not absolutely star Countable); (4) assuming \(2^{\aleph _0 } = 2^{\aleph _1 }\), there exists an absolutely star Countable normal Space having a regular closed subSpace which is not star Countable (hence not absolutely star Countable).
