Itô type stochastic fuzzy differential equations with delay

Systems and Control Letters

Volumn 61, Issue 6, 2012, Pages 692-701

  Malinowski, Marek T ^a  

^a UNIVERSITY OF ZIELONA GÓRA   (Poland)

Author keywords

Fuzziness and randomness in modeling; Fuzzy random variable; Fuzzy stochastic It integral; Fuzzy stochastic Lebesgue Aumann integral; Fuzzy stochastic process; Stochastic fuzzy differential equation; Stochastic fuzzy differential equation with delay; Stochastic fuzzy functional differential equation

Indexed keywords

FUNCTIONAL DIFFERENTIAL EQUATIONS; FUZZY RANDOM VARIABLE; FUZZY STOCHASTIC LEBESGUE-AUMANN INTEGRALS; FUZZY STOCHASTIC PROCESS; STOCHASTIC FUZZY DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATIONS; POPULATION STATISTICS; RANDOM PROCESSES;

STOCHASTIC SYSTEMS;

EID: 84860359608     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2012.02.012     Document Type: Article

References (51)

1. I.I. Gihman, and A.V. Skorohod Stochastic Differential Equations 1972 Springer-Verlag Berlin
2. X. Mao Stochastic Differential Equations and Applications 2007 Horwood Publishing Limited Chichester
3. B. Oksendal Stochastic Differential Equations: An Introduction with Applications 2003 Springer-Verlag Berlin
4. C.V. Negoita, and D.A. Ralescu Applications of Fuzzy Sets to System Analysis 1975 Wiley New York
5. L.A. Zadeh Fuzzy sets Inf. Control 8 1965 338 353
6. L.A. Zadeh Fuzzy sets as a basis for a theory of possibility Fuzzy Sets and Systems 1 1978 3 28
7. H.-J. Zimmermann Fuzzy Set Theory and its Applications 1996 Kluwer Academic Publishers Boston
8. B. Bede, T. Gnana Bhaskar, and V. Lakshmikantham Perspectives of fuzzy initial value problems Commun. Appl. Anal. 11 2007 339 358
9. P. Diamond, and P. Kloeden Metric Spaces of Fuzzy Sets: Theory and Applications 1994 World Scientific Singapore
10. T. Gnana Bhaskar, V. Lakshmikantham, and J. Vasundhara Devi Revisiting fuzzy differential equations Nonlinear Anal. TMA 58 2004 351 358
11. O. Kaleva Fuzzy differential equations Fuzzy Sets and Systems 24 1987 301 317
12. O. Kaleva A note on fuzzy differential equations Nonlinear Anal. TMA 64 2006 895 900
13. V. Lakshmikantham, and R.N. Mohapatra Theory of Fuzzy Differential Equations and Inclusions 2003 Taylor & Francis London
14. W. Fei Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients Inform. Sci. 177 2007 4329 4337
15. Y. Feng Fuzzy stochastic differential systems Fuzzy Sets and Systems 115 2000 351 363
16. M.T. Malinowski On random fuzzy differential equations Fuzzy Sets and Systems 160 2009 3152 3165
17. M.T. Malinowski Existence theorems for solutions to random fuzzy differential equations Nonlinear Anal. TMA 73 2010 1515 1532
18. M.T. Malinowski Random fuzzy differential equations under generalized Lipschitz condition Nonlinear Anal. RWA 13 2012 860 881
19. J.H. Kim On fuzzy stochastic differential equations J. Korean Math. Soc. 42 2005 153 169
20. M.T. Malinowski Strong solutions to stochastic fuzzy differential equations of Itô type Math. Comput. Modelling 55 2012 918 928
21. M.T. Malinowski, and M. Michta Fuzzy stochastic integral equations Dynam. Systems Appl. 19 2010 473 494
22. M.T. Malinowski, and M. Michta Stochastic fuzzy differential equations with an application Kybernetika 47 2011 123 143
23. M.T. Malinowski, and M. Michta Fuzzy stochastic integral equations driven by martingales S. Li, Nonlinear Maths for Uncertainty and its Appli., AISC 100 2011 Springer Berlin 143 150
24. M. Michta On set valued stochastic integrals and fuzzy stochastic equation Fuzzy Sets and Systems 177 2011 1 19
25. Y. Ogura On stochastic differential equations with fuzzy set coefficients D. Dubois, Soft Methods for Handling Variability and Imprecision 2008 Springer Berlin 263 270
26. J. Hale Theory of Functional Differential Equations 1977 Springer Verlag Berlin
27. J.A.D. Appleby, and X. Mao Stochastic stabilisation of functional differential equations Systems Control Lett. 54 2005 1069 1081
28. X. Li, and X. Fu Stability analysis of stochastic functional differential equations with infinite delay and its application to recurrent neural networks J. Comput. Appl. Math. 234 2010 407 417
29. K. Liu, and X. Xia On the exponential stability in mean square of neutral stochastic functional differential equations Systems Control Lett. 37 1999 207 215
30. X. Mao Robustness of stability of nonlinear systems with stochastic delay perturbations Systems Control Lett. 19 1992 391 400
31. X. Mao Exponential stability in mean square of neutral stochastic differential functional equations Systems Control Lett. 26 1995 245 251
32. X. Mao, N. Koroleva, and A. Rodkina Robust stability of uncertain stochastic differential delay equations Systems Control Lett. 35 1998 325 336
33. X. Mao, and M. Riedle Mean square stability of stochastic Volterra integro-differential equations Systems Control Lett. 55 2006 459 465
34. S.-E.A. Mohammed Stochastic Functional Differential Equations 1984 Pitman Publishing Limited Boston
35. Y. Ren, S. Lu, and N. Xia Remarks on the existence and uniqueness of the solutions to stochastic functional differential equations with infinite delay J. Comput. Appl. Math. 220 2008 364 372
36. Y. Ren, and N. Xia Existence, uniqueness and stability of the solutions to neutral stochastic functional differential equations with infinite delay Appl. Math. Comput. 210 2009 72 79
37. F. Wei, and K. Wang The existence and uniqueness of the solution for stochastic functional differential equations with infinite delay J. Math. Anal. Appl. 331 2007 516 531
38. F. Wu, S. Hu, and Ch. Huang Robustness of general decal stability on nonlinear neutral stochastic functional differential equations with infinite delay Systems Control Lett. 59 2010 195 202
39. F. Wu, X. Mao, and S. Hu Stochastic suppression and stabilization of functional differential equations Systems Control Lett. 59 2010 745 753
40. D. Xu, Z. Yang, and Y. Huang Existence-uniqueness and continuation theorems for stochastic functional differential equations J. Differential Equations 245 2008 1681 1703
41. Z. Yang, E. Zhu, Y. Xu, and Y. Tan Razumikhin-type theorems on exponential stability of stochastic functional differential equations with infinite delay Acta Appl. Math. 111 2010 219 231
42. S. Zhou, Z. Wang, and D. Feng Stochastic functional differential equations with infinite delay J. Math. Anal. Appl. 357 2009 416 426
43. V.B. Kolmanovskii, and A. Myshkis Applied Theory of Functional Differential Equations 1992 Kluwer Academic Publishers Dordrecht
44. F. Hiai, and H. Umegaki Integrals, conditional expectation, and martingales of multivalued functions J. Multivariate Anal. 7 1977 149 182
45. M.L. Puri, and D.A. Ralescu Fuzzy random variables J. Math. Anal. Appl. 114 1986 409 422
46. DE [ 0, 1 ] representation of random upper semicontinuous functions Proc. Amer. Math. Soc. 130 2002 3237 3242
47. M. Kisielewicz Differential Inclusions and Optimal Control 1991 Kluwer Academic Publishers Dordrecht
48. S. Hu, and N. Papageorgiou Handbook of Multivalued Analysis, Vol. I: Theory 1997 Kluwer Academic Publishers Boston
49. S. Li, and A. Ren Representation theorems, set-valued and fuzzy set-valued Itô integral Fuzzy Sets and Systems 158 2007 949 962
50. J. Zhang Set-valued stochastic integrals with respect to a real valued martingale D. Dubois, Soft Methods for Handling Variability and Imprecision 2008 Springer Berlin 253 259
51. S.-E.A. Mohammed Stochastic differential equations with memory: theory, examples and applications Progress in Probability, Stochastic Analysis and Related Topics 6. The Geido Workshop 1998 Birkhäuser