Strong solutions to stochastic fuzzy differential equations of Itô type

Mathematical and Computer Modelling

Volumn 55, Issue 3-4, 2012, Pages 918-928

  Malinowski, Marek T ^a  

^a UNIVERSITY OF ZIELONA GÓRA   (Poland)

Author keywords

Fuzziness and randomness in modelling; Fuzzy random variable; Fuzzy stochastic It integral; Fuzzy stochastic Lebesgue Aumann integral; Fuzzy stochastic process; Stochastic fuzzy differential equation; Stochastic fuzzy integral equation

Indexed keywords

FUZZINESS AND RANDOMNESS IN MODELLING; FUZZY DIFFERENTIAL EQUATIONS; FUZZY INTEGRAL; FUZZY RANDOM VARIABLE; FUZZY STOCHASTIC LEBESGUE-AUMANN INTEGRAL; FUZZY STOCHASTIC PROCESS;

BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; RANDOM VARIABLES; STOCHASTIC SYSTEMS;

INTEGRAL EQUATIONS;

EID: 84855205569     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2011.09.018     Document Type: Article

References (36)

1. Gihman I.I., Skorohod A.V. Stochastic Differential Equations 1972, Springer-Verlag, Berlin.
2. Øksendal B. Stochastic Differential Equations: An Introduction with Applications 2003, Springer Verlag, Berlin.
3. Zadeh L.A. Fuzzy sets. Inform. Control 1965, 8:338-353.
4. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1978, 1:3-28.
5. Zimmermann H.J. Fuzzy Set Theory and its Applications 1991, Kluwer Academic Publishers, Boston.
6. Balasubramaniam P., Muralisankar S. Existence and uniqueness of fuzzy solution for semilinear fuzzy integrodifferential equations with nonlocal conditions. Comput. Math. Appl. 2004, 47:1115-1122.
7. Diamond P., Kloeden P. Metric Spaces of Fuzzy Sets: Theory and Applications 1994, World Scientific, Singapore.
8. Gong Z., Shao Y. Global existence and uniqueness of solutions for fuzzy differential equations under dissipative-type conditions. Comput. Math. Appl. 2008, 56:2716-2723.
9. Guo M., Xue X., Li R. The oscillation of delay differential inclusions and fuzzy biodynamic models. Math. Comput. Modelling 2003, 37:651-658.
10. Kaleva O. Fuzzy differential equations. Fuzzy Sets and Systems 1987, 24:301-317.
11. Lakshmikantham V., Mohapatra R.N. Theory of Fuzzy Differential Equations and Inclusions 2003, Taylor & Francis, London.
12. Pederson S., Sambandham M. Numerical solution to hybrid fuzzy systems. Math. Comput. Modelling 2007, 45:1133-1144.
13. Song S., Wu C., Lee E.S. Asymptotic equilibrium and stability of fuzzy differential equations. Comput. Math. Appl. 2005, 49:1267-1277.
14. Song S., Wu C., Xue X. Existence and uniqueness of cauchy problem for fuzzy differential equations under dissipative conditions. Comput. Math. Appl. 2006, 51:1483-1492.
15. Fei W. Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients. Inform. Sci. 2007, 177:4329-4337.
16. Feng Y. Fuzzy stochastic differential systems. Fuzzy Sets and Systems 2000, 115:351-363.
17. Malinowski M.T. On random fuzzy differential equations. Fuzzy Sets and Systems 2009, 160:3152-3165.
18. Malinowski M.T. Existence theorems for solutions to random fuzzy differential equations. Nonlinear Anal. TMA 2010, 73:1515-1532.
19. Malinowski M.T. Random fuzzy differential equations under generalized Lipschitz condition. Nonlinear Anal. RWA 2011, 10.1016/j.nonrwa.2011.08.022.
20. Li J., Li Sh. Itô type set-valued stochastic differential equation. J. Uncertain Syst. 2009, 3:52-63.
21. Li J., Li Sh., Ogura Y. Strong solution of Itô type set-valued stochastic differential equation. Acta Math. Sin. (Engl. Ser.) 2010, 26:1739-1748.
22. Malinowski M.T., Michta M. Stochastic set differential equations. Nonlinear Anal. TMA 2010, 72:1247-1256.
23. Malinowski M.T., Michta M. Set-valued stochastic integral equations. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 2011, 18:473-492.
24. Mitoma I., Okazaki Y., Zhang J. Set-valued stochastic differential equation in M-type 2 Banach space. Commun. Stoch. Anal. 2010, 4:215-237.
25. Zhang J., Li Sh., Mitoma I., Okazaki Y. On the solutions of set-valued stochastic differential equations in M-type 2 Banach spaces. Tohoku Math. J. 2009, 61:417-440.
26. Kim J.H. On fuzzy stochastic differential equations. J. Korean Math. Soc. 2005, 42:153-169.
27. Malinowski M.T., Michta M. Fuzzy stochastic integral equations. Dynam. Systems Appl. 2010, 19:473-494.
28. Malinowski M.T., Michta M. Stochastic fuzzy differential equations with an application. Kybernetika 2011, 47:123-143.
29. Ogura Y. On stochastic differential equations with fuzzy set coefficients. Soft Methods for Handling Variability and Imprecision 2008, 263-270. Springer, Berlin. D. Dubois (Ed.).
30. Zhang J. Set-valued stochastic integrals with respect to a real valued martingale. Soft Methods for Handling Variability and Imprecision 2008, 253-259. Springer, Berlin. D. Dubois (Ed.).
31. Hiai F., Umegaki H. Integrals, conditional expectation, and martingales of multivalued functions. J. Multivariate Anal. 1977, 7:149-182.
32. Puri M.L., Ralescu D.A. Fuzzy random variables. J. Math. Anal. Appl. 1986, 114:409-422.
33. Colubi A., Domínguez-Menchero J.S., López-Díaz M., Ralescu D.A. A DE[0,1] representation of random upper semicontinuous functions. Proc. Amer. Math. Soc. 2002, 130:3237-3242.
34. Kisielewicz M. Differential Inclusions and Optimal Control 1991, Kluwer Academic Publishers, Dordrecht.
35. Li Sh., Ren A. Representation theorems, set-valued and fuzzy set-valued Ito integral. Fuzzy Sets and Systems 2007, 158:949-962.
36. Negoita C.V., Ralescu D.A. Applications of Fuzzy Sets to System Analysis 1975, Wiley, New York.