Existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian condition

DOI10.1016/J.NA.2012.08.015zbMath1255.60093OpenAlexW2004914285MaRDI QIDQ715689

Weiyin Fei

Publication date: 31 October 2012

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2012.08.015

zbMATH Keywords

fuzzy random variableslocal martingalesfuzzy stochastic Itô integralfuzzy stochastic differential equationsnon-Lipschitzian condition

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Ordinary differential equations and systems with randomness (34F05) Fuzzy real analysis (26E50)

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On solutions to set-valued and fuzzy stochastic differential equations ⋮ On solutions to fuzzy stochastic differential equations with local martingales ⋮ On existence and uniqueness of solutions to uncertain backward stochastic differential equations ⋮ Properties of solutions to stochastic set differential equations under non-Lipschitzian coefficients ⋮ Iterative method for non-adapted fuzzy stochastic differential equations ⋮ On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability ⋮ The fuzzy characterizing function of the distribution of a random fuzzy number ⋮ Donsker's fuzzy invariance principle under the Lindeberg condition ⋮ Existence and stability of solutions of fuzzy fractional stochastic differential equations with fractional Brownian motions

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