nach oben

Fuzzy Optimization and Decision Making

Erschienen in:

01.12.2014

Almost sure stability for uncertain differential equation

verfasst von: Hongjian Liu, Hua Ke, Weiyin Fei

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 4/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Uncertain differential equation is a type of differential equation driven by Liu process. So far, concepts of stability and stability in mean for uncertain differential equations have been proposed. This paper aims at providing a concept of almost sure stability for uncertain differential equation. A sufficient condition is given for an uncertain differential equation being almost surely stable, and some examples are given to illustrate the effectiveness of the sufficient condition.

Vorheriger Artikel The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Chen, X. (2011). American option pricing formula for uncertain financial market. International Journal of Operations Research, 8(2), 32–37.

Chen, X., & Gao, J. (2013). Uncertain term structure model of interest rate. Soft Computing, 17(4), 597–604.CrossRefMathSciNetMATH

Chen, X., & Liu, B. (2010). Existence and uniqueness theorem for uncertain differential equations. Fuzzy Optimization and Decision Making, 9(1), 69–81.CrossRefMathSciNetMATH

Chen, X., & Ralescu, D. A. (2013). Liu process and uncertain calculus. Journal of Uncertainty Analysis and Applications, 1, Article 3.

Gao, Y. (2012). Existence and uniqueness theorem on uncertain differential equations with local Lipschitz condition. Journal of Uncertain Systems, 6(3), 223–232.

Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263–292.CrossRefMATH

Liu, B. (2007). Uncertainty Theory (2nd ed.). Berlin: Springer.MATH

Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.

Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.

Liu, B. (2010). Uncertainty theory: A branch of mathematics for modeling human uncertainty. Berlin: Springer.CrossRef

Liu, B. (2012). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6(1), 3–10.

Liu, B. (2013). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1, Article 1.

Liu, B. (2014). Uncertainty distribution and independence of uncertain processes. Fuzzy Optimization and Decision Making, to be published.

Liu, Y. H. (2012). An analytic method for solving uncertain differential equations. Journal of Uncertain Systems, 6(4), 244–249.

Liu, H. J., & Fei, W. Y. (2012). Existence and uniqueness of solutions to uncertain functional differential equations. In: Proceedings of the ninth international conference on fuzzy systems and knowledge discovery (pp. 63–66).

Liu, H. J., & Fei, W. Y. (2013). Neutral uncertain delay differential equations. Information. An International Interdisciplinary Journal, 16(2(A)), 1225–1232.

Liu, Y. H., Chen, X., & Ralescu, D. A. (2013). Uncertain currency model and currency option pricing. International Journal of Intelligent Systems, to be published.

Peng, J., & Yao, K. (2011). A new option pricing model for stocks in uncertainty markets. International Journal of Operations Research, 8(2), 18–26.MathSciNet

Sheng, Y. (2013). Stability in the \(p\)th moment for uncertain differential equation. Journal of Intelligent and Fuzzy Systems, to be published.

Yao, K. (2012a). Uncertain calculus with renewal process. Fuzzy Optimization and Decision Making, 11(3), 285–297.CrossRefMathSciNetMATH

Yao, K. (2012b). No-arbitrage determinant theorems on mean-reverting stock model in uncertain market. Knowledge-Based Systems, 35, 259–263.CrossRef

Yao, K. (2013a). Extreme values and integral of solution of uncertain differential equation. Journal of Uncertainty Analysis and Applications, 1, Article 2.

Yao, K. (2013b). A type of uncertain differential equations with analytic solution. Journal of Uncertainty Analysis and Applications, 1, Article 8.

Yao, K., & Chen, X. (2013). A numerical method for solving uncertain differential equations. Journal of Intelligent and Fuzzy Systems, 25(3), 825–832.MathSciNetMATH

Yao, K., & Sheng Y. (2013). Stability in mean for uncertain differential equation. http://orsc.edu.cn/online/120611

Yao, K., Gao, J., & Gao, Y. (2013). Some stability theorems of uncertain differential equation. Fuzzy Optimization and Decision Making, 12(1), 3–13.CrossRefMathSciNet

Titel: Almost sure stability for uncertain differential equation
verfasst von: Hongjian Liu
Hua Ke
Weiyin Fei
Publikationsdatum: 01.12.2014
Verlag: Springer US
Erschienen in: Fuzzy Optimization and Decision Making / Ausgabe 4/2014
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-014-9188-y

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 4/2014

The existence and uniqueness of fuzzy solutions for hyperbolic partial differential equations

On Arrow–Sen style equivalences between rationality conditions for fuzzy choice functions

A semantic study of the first-order predicate logic with uncertainty involved

Renewal reward process for $$T$$ T -related fuzzy random variables on $$(\mathbb {R}^{p}, \mathbb {R}^{q})$$ ( R p , R q )

Multi-objective optimization in uncertain random environments