JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
ON FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS
KIM JAI HEUI;
  PDF(new window)
 Abstract
A fuzzy stochastic differential equation contains a fuzzy valued diffusion term which is defined by stochastic integral of a fuzzy process with respect to 1-dimensional Brownian motion. We prove the existence and uniqueness of the solution for fuzzy stochastic differential equation under suitable Lipschitz condition. To do this we prove and use the maximal inequality for fuzzy stochastic integrals. The results are illustrated by an example.
 Keywords
fuzzy martingale;fuzzy stochastic differential equation;
 Language
English
 Cited by
1.
On solutions to fuzzy stochastic differential equations with local martingales, Systems & Control Letters, 2014, 65, 96  crossref(new windwow)
2.
Formulation of Stochastic Investment Model of a Stock Market, Journal of the Indian Society for Probability and Statistics, 2016, 17, 1, 25  crossref(new windwow)
3.
Some properties of strong solutions to stochastic fuzzy differential equations, Information Sciences, 2013, 252, 62  crossref(new windwow)
4.
Stochastic differential equations with fuzzy drift and diffusion, Fuzzy Sets and Systems, 2013, 230, 53  crossref(new windwow)
5.
Existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian condition, Nonlinear Analysis: Theory, Methods & Applications, 2013, 76, 202  crossref(new windwow)
6.
Itô type stochastic fuzzy differential equations with delay, Systems & Control Letters, 2012, 61, 6, 692  crossref(new windwow)
7.
Strong solutions to stochastic fuzzy differential equations of Itô type, Mathematical and Computer Modelling, 2012, 55, 3-4, 918  crossref(new windwow)
8.
Lebesgues-Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes, Applied Mathematics, 2015, 06, 13, 2199  crossref(new windwow)
9.
On set-valued stochastic integrals and fuzzy stochastic equations, Fuzzy Sets and Systems, 2011, 177, 1, 1  crossref(new windwow)
10.
Numerical solution of fuzzy stochastic differential equation, Journal of Intelligent & Fuzzy Systems, 2016, 31, 1, 555  crossref(new windwow)
 References
1.
R. J. Aumann, Integrals of set-valued functions, J. Math. Anal. Appl. 12 (1965), 1-12 crossref(new window)

2.
A. J. Baddeley, Stochastic geometry and image analysis, CWI Newslett. 4 (1984), 2-20

3.
J. Ban, Radon-Nikodym theorem and conditional expectation, Fuzzy Sets and Systems. 34 (1990), 383-392 crossref(new window)

4.
P. Diamond, Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy Sets and Systems. 129 (2002), 65-71 crossref(new window)

5.
F. Hiai, Convergence of conditional expectations and strong laws of large numbers for multivalued random variables, Trans. Amer. Math. Soc. 291 (1985), no. 2, 613-627 crossref(new window)

6.
F. Hiai and H. Umegaki, Integrals, conditional expectations, and martingales of multivalued functions, J. Multivar. Anal. 7 (1977), 149-182 crossref(new window)

7.
M. Hukuhara, Introduction des applications measurables dont la valeur est un compact convexe, Funkcialaj. Ekvacioj. 10 (1967), 205-223

8.
E. J. Jung and J. H. Kim, On set-valued stochastic integrals, Stochastic Analysis and Applications. 21 (2003), No. 2, 401-418 crossref(new window)

9.
O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems. 24 (1987), 301-317 crossref(new window)

10.
B. K. Kim and J. H. Kim, Stochastic integrals of set-valued processes and fuzzy processes, J. Math. Anal. Appl. 236 (1999), No. 2, 480-502 crossref(new window)

11.
B. Oksendal, Stochastic Differential Equations, Springer-Verlag, 1998

12.
M. L. Puri and D. A. Ralescu, Fuzzy random variables, J. Math. Anal. Appl. 114 (1986), 406-422

13.
M. Stojakovic, Fuzzy random variable, expectation, and martingales, J. Math. Anal. Appl. 184 (1994), 594-606 crossref(new window)

14.
D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Springer-Verlag, New York, 1979