On stochastic differential equations with fuzzy set coefficients

Advances in Soft Computing

Volumn 48, Issue , 2008, Pages 263-270

  Ogura, Yukio ^a  

^a SAGA UNIVERSITY   (Japan)

Author keywords

Fuzzy set coefficients; Random fuzzy sets; Random sets; Set coefficients; Stochastic differential equation

Indexed keywords

EID: 58149131672     PISSN: 16153871     EISSN: 18600794     Source Type: Book Series    
DOI: 10.1007/978-3-540-85027-4_32     Document Type: Article

References (14)

1. Ahmed, N.U.: Nonlinear stochastic differential inclusions on Banach space. Stochastic Anal. Appl. 12, 1-10 (1994)
2. Black, F., Scholes, M.: The pricing of options and corporate liabilities. Scottish J. Political Econ. 81, 637-654 (1973)
3. Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes, 2nd edn. North-Holland Mathematical Library, vol. 24. North-Holland, Amsterdam (1989)
4. Itô, K.: On a stochastic integral equation. Proc. Japan Acad. 22, 32-35 (1946)
5. Jung, E.J., Kim, J.H.: On set-valued stochastic integrals. Stochastic Anal. Appl. 21, 401-418 (2003)
6. Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics, vol. 113. Springer, New York (1988)
7. Kisielewicz, M.: Properties of solution set of stochastic inclusions. J. Appl. Math. Stochastic Anal. 6, 217-236 (1993)
8. Kisielewiz, M., Michta, M., Motyl, J.: Set valued approach to Stochastic control, Part 1: Existence and regularity properties. Dynamic Systems Appl. 12, 405-432 (2003); Part 2: Viability and semimartingale issues 12, 433-466
9. Li, S., Ogura, Y., Kreinovich, V.: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables. Theory and Decision Library. Series B: Mathematical and Statistical Methods, vol. 43. Kluwer Academic Publishers Group, Dordrecht (2002)
10. Merton, R.C.: Optimum consumption and portfolio rules in a continuous time model. J. Econom. Theory 3, 373-413 (1971)
11. Ogura, Y.: On stochastic differential equations with set coefficients and the Black-Scholes model. In: Proceedings of the 8th International Conference on Intelligent Technologies (In-Tech 2007, Sydney, Australia), pp. 300-304 (2007)
12. Øksendal, B.: Stochastic Differential Equations. Universitext. Springer, Berlin (1985)
13. Stroock, D.W., Varadhan, S.R.S.: On the support of diffusion processes with application to the strong maximum principle. In: Proceedings of Sixth Berkeley Symp Math Statist Prob III, pp. 333-359. Univ. California Press, Berkeley (1972)
14. Yamada, T., Ogura, Y.: On the strong comparison theorem for solutions of stochastic differential equations. Z Wharsch verw Gebiete 56, 3-19 (1981)