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On fuzzy stochastic differential equations

김재희
대한수학회 (The Korean Mathematical Society)|2005.01|대한수학회지 (Journal of the KMS)|제42권 제1호|pp. 153-169

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Abstract

A fuzzy stochastic di??erential equation contains a fuzzy valued di??usion term which is de¯ned 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 stochas-tic di??erential 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.

참고문헌 (11)

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  3. "Radon-Nikodym theorem and conditional expectation", 34, pp.383~392 (1990)
  4. "Brief note on the variation of constants formula for fuzzy dierentialequations", 129, pp.65~71 (2002)
  5. "Convergence of conditional expectations and strong laws of large numbersfor multivalued random variables", 291(2), pp.613~627 (1985)
  6. "Introduction des applications measurables dont la valeur est uncompact convexe", 10, pp.205~223 (1967)
  7. "On set-valued stochastic integrals", 21(2), pp.401~418 (2003)
  8. "Fuzzy dierential equations", 24, pp.301~317 (1987)
  9. "Stochastic integrals of set-valued processes and fuzzyprocesses", 236(2), pp.480~502 (1999)
  10. B. ksendal, "Stochastic Dierential Equations" (1998)
  11. "Fuzzy random variables", 114, pp.406~422 (1986)

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