On multivalued martingales whose values may be unbounded: martingale selectors and Mosco convergence
Journal of Multivariate Analysis
Stochastic differential equations (3rd ed.): an introduction with applications
Stochastic differential equations (3rd ed.): an introduction with applications
Decomposition and representation theorem of set-valued amarts
International Journal of Approximate Reasoning
The space of fuzzy set-valued square integrable martingales
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
On solutions of stochastic differential equations with parameters modeled by random sets
International Journal of Approximate Reasoning
On set-valued stochastic integrals and fuzzy stochastic equations
Fuzzy Sets and Systems
Fuzzy set-valued stochastic Lebesgue integral
Fuzzy Sets and Systems
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In this paper, we shall present representation theorems of set-valued martingales and set-valued processes of finite variation with continuous time. We shall also obtain a representation theorem of a predictable set-valued stochastic process. We shall give a new definition of Ito integral of a set-valued stochastic process with respect to a Brownian motion based on the work [E.J. Jung, J.H. Kim, On set-valued stochastic integrals, Stochastic Anal. Appl. 21(2) (2003) 401-418.]. We shall also discuss some properties of set-valued Ito integral, especially the presentation theorem of set-valued Ito integral. Finally, we extend some of above results to the fuzzy set-valued case.