Strong solutions to stochastic fuzzy differential equations of Itô type

DOI10.1016/j.mcm.2011.09.018zbMath1255.34004OpenAlexW1984245156MaRDI QIDQ1931010

Marek T. Malinowski

Publication date: 24 January 2013

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2011.09.018

zbMATH Keywords

Aumann integralfuzzy random variablefuzzy stochastic processfuzziness and randomness in modellingfuzzy stochastic Itô integralstochastic fuzzy differential equationfuzzy stochastic Lebesguestochastic fuzzy integral equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Fuzzy ordinary differential equations (34A07)

Related Items (34)

Interval-valued functional differential equations under dissipative conditions ⋮ Finite-time reliable filtering for T-S fuzzy stochastic jumping neural networks under unreliable communication links ⋮ Two-Parameter Fuzzy-Valued Stochastic Integrals and Equations ⋮ On solutions to set-valued and fuzzy stochastic differential equations ⋮ Fuzzy stochastic differential equations driven by semimartingales-different approaches ⋮ Fuzzy stochastic differential equations driven by fractional Brownian motion ⋮ Sensitivity of option prices via fuzzy Malliavin calculus ⋮ Set-valued and fuzzy stochastic differential equations in M-type 2 Banach spaces ⋮ An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion ⋮ Stochastic fuzzy differential equations of a nonincreasing type ⋮ Set-valued stochastic integral equations driven by martingales ⋮ Itô type stochastic fuzzy differential equations with delay ⋮ On random fuzzy functional differential equations ⋮ On solutions to fuzzy stochastic differential equations with local martingales ⋮ Interval-valued functional integro-differential equations ⋮ Fuzzy stochastic differential equations of decreasing fuzziness: Approximate solutions ⋮ Properties of solutions to stochastic set differential equations under non-Lipschitzian coefficients ⋮ Iterative method for non-adapted fuzzy stochastic differential equations ⋮ Some properties of strong solutions to stochastic fuzzy differential equations ⋮ On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability ⋮ Random fuzzy fractional integral equations -- theoretical foundations ⋮ On a new set-valued stochastic integral with respect to semimartingales and its applications ⋮ The interrelation between stochastic differential inclusions and set-valued stochastic differential equations ⋮ Approximation schemes for fuzzy stochastic integral equations ⋮ Multiple solutions of ordinary differential systems with min-max terms and applications to the fuzzy differential equations ⋮ Stochastic integrals and stochastic equations in set-valued and fuzzy-valued frameworks ⋮ On Equations with a Fuzzy Stochastic Integral with Respect to Semimartingales ⋮ On the solutions for box differential equations under generalized Hukuhara derivative ⋮ Fuzzy and Set-Valued Stochastic Differential Equations with Solutions of Decreasing Fuzziness ⋮ On fuzzy type-1 and type-2 stochastic ordinary and partial differential equations and numerical solution ⋮ Existence and stability of solutions of fuzzy fractional stochastic differential equations with fractional Brownian motions ⋮ Existence of solutions for implicit fuzzy differential inclusions ⋮ Results on initial value problems for random fuzzy fractional functional differential equations ⋮ Fuzzy stochastic differential equations of decreasing fuzziness: Non-Lipschitz coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The oscillation of delay differential inclusions and fuzzy biodynamics models
• Strong solution of Itô type set-valued stochastic differential equation
• Representation theorems, set-valued and fuzzy set-valued Itô integral
• Existence theorems for solutions to random fuzzy differential equations
• On random fuzzy differential equations
• On the solutions of set-valued stochastic differential equations in M-type 2 Banach spaces
• Integrals, conditional expectations, and martingales of multivalued functions
• Fuzzy sets as a basis for a theory of possibility
• Fuzzy stochastic differential systems
• Existence and uniqueness of fuzzy solution for semilinear fuzzy integrodifferential equations with nonlocal conditions
• Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients
• Asymptotic equilibrium and stability of fuzzy differential equations
• Global existence and uniqueness of solutions for fuzzy differential equations under dissipative-type conditions
• Existence and uniqueness of Cauchy problem for fuzzy differential equations under dissipative conditions
• Numerical solution to hybrid fuzzy systems
• Stochastic set differential equations
• A $D_E[0,1$ representation of random upper semicontinuous functions]
• ON FUZZY STOCHASTIC DIFFERENTIAL EQUATIONS
• Fuzzy sets
• Fuzzy random variables
• Fuzzy differential equations
• Stochastic differential equations. An introduction with applications.

This page was built for publication: Strong solutions to stochastic fuzzy differential equations of Itô type