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

[1]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[2]  F. Hiai,et al.  Integrals, conditional expectations, and martingales of multivalued functions , 1977 .

[3]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[4]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[5]  B. Øksendal Stochastic differential equations : an introduction with applications , 1987 .

[6]  Osmo Kaleva Fuzzy differential equations , 1987 .

[7]  P. Protter Stochastic integration and differential equations , 1990 .

[8]  M. Kisielewicz Differential Inclusions and Optimal Control , 1991 .

[9]  X. Mao,et al.  Exponential Stability of Stochastic Di erential Equations , 1994 .

[10]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

[11]  Yuhu Feng,et al.  Fuzzy stochastic differential systems , 2000, Fuzzy Sets Syst..

[12]  Ana Colubi,et al.  A _{}[0,1] representation of random upper semicontinuous functions , 2002 .

[13]  V. Lakshmikantham,et al.  Theory of Fuzzy Differential Equations and Inclusions , 2003 .

[14]  Weiyin Fei,et al.  Doob's stopping theorem for fuzzy (super, sub) martingales with discrete time , 2003, Fuzzy Sets Syst..

[15]  W. Fei,et al.  Doob's Decomposition Theorem for Fuzzy (Super) Submartingales , 2004 .

[16]  J. Kim ON FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS , 2005 .

[17]  Weiyin Fei Regularity and stopping theorem for fuzzy martingales with continuous parameters , 2005, Inf. Sci..

[18]  W. Fei On the Theory of (Dual) Projection for Fuzzy Stochastic Processes , 2005 .

[19]  Ana Colubi,et al.  A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing , 2006, Comput. Stat. Data Anal..

[20]  Pedro Terán Agraz On Borel measurability and large deviations for fuzzy random variables , 2006, Fuzzy Sets Syst..

[21]  Dan A. Ralescu,et al.  Overview on the development of fuzzy random variables , 2006, Fuzzy Sets Syst..

[22]  Weiyin Fei,et al.  A Generalization of Bihari's inequality and Fuzzy Random Differential Equations with Non-Lipschitz Coefficients , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[23]  Li Guan,et al.  Fuzzy set-valued Gaussian processes and Brownian motions , 2007, Inf. Sci..

[24]  Aihong Ren,et al.  Representation theorems, set-valued and fuzzy set-valued Ito integral , 2007, Fuzzy Sets Syst..

[25]  Weiyin Fei,et al.  Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients , 2007, Inf. Sci..

[26]  Yukio Ogura,et al.  On Stochastic Differential Equations with Fuzzy Set Coefficients , 2008, SMPS.

[27]  Marek T. Malinowski,et al.  On random fuzzy differential equations , 2009, Fuzzy Sets Syst..

[28]  Ana Colubi,et al.  Estimation of a simple linear regression model for fuzzy random variables , 2009, Fuzzy Sets Syst..

[29]  M. T. Malinowski Existence theorems for solutions to random fuzzy differential equations , 2010 .

[30]  M. T. Malinowski,et al.  Stochastic set differential equations , 2010 .

[31]  I. Mitoma,et al.  SET-VALUED STOCHASTIC DIFFERENTIAL EQUATION IN M-TYPE 2 BANACH SPACE , 2010 .

[32]  Marek T. Malinowski,et al.  FUZZY STOCHASTIC INTEGRAL EQUATIONS , 2010 .

[33]  Mariusz Michta,et al.  On set-valued stochastic integrals and fuzzy stochastic equations , 2011, Fuzzy Sets Syst..

[34]  Marek T. Malinowski,et al.  Stochastic fuzzy differential equations with an application , 2011, Kybernetika.

[35]  M. T. Malinowski Random fuzzy differential equations under generalized Lipschitz condition , 2012 .

[36]  Marek T. Malinowski,et al.  Strong solutions to stochastic fuzzy differential equations of Itô type , 2012, Math. Comput. Model..

[37]  Marek T. Malinowski,et al.  Itô type stochastic fuzzy differential equations with delay , 2012, Syst. Control. Lett..

[38]  W. Fei,et al.  On solutions to stochastic set differential equations of It^o type under the non-Lipschitzian condition , 2013 .

[39]  Marek T. Malinowski,et al.  Some properties of strong solutions to stochastic fuzzy differential equations , 2013, Inf. Sci..