Mean square Hyers-Ulam stability of stochastic differential equations driven by Brownian motion

DOI10.1186/s13662-016-1002-4zbMath1419.34156OpenAlexW2538457106WikidataQ59468639 ScholiaQ59468639MaRDI QIDQ1628143

Xiangkui Zhao

Publication date: 3 December 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-016-1002-4

zbMATH Keywords

Brownian motionstochastic differential equationsHyers-Ulam stabilitysubstitution method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability of solutions to ordinary differential equations (34D20) Ordinary differential equations and systems with randomness (34F05)

Related Items

Ulam–Hyers–Rassias stability of neutral stochastic functional differential equations ⋮ On stability of stochastic differential equations with random impulses driven by Poisson jumps ⋮ Existence and Hyers-Ulam stability of random impulsive stochastic functional differential equations with finite delays ⋮ Ulam-Hyers-Rassias stability of a nonlinear stochastic Ito-Volterra integral equation ⋮ Existence and Hyers-Ulam stability of random impulsive stochastic functional integrodifferential equations with finite delays ⋮ Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods ⋮ Hyers–Ulam stability for equations with differences and differential equations with time-dependent and periodic coefficients

Cites Work

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• Existence, uniqueness and stability of random impulsive fractional differential equations
• Hyers-Ulam stability and discrete dichotomy for difference periodic systems
• New concepts and results in stability of fractional differential equations
• Ulam's type stability of impulsive ordinary differential equations
• Hyers-Ulam stability and discrete dichotomy
• Hyers-Ulam stability of additive set-valued functional equations
• On the Hyers-Ulam stability of the linear differential equation
• Hyers-Ulam stability of linear differential equations of second order
• Hyers-Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems
• Ulam-Hyers stability of dynamic equations on time scales via Picard operators
• Hyers-Ulam stability of linear differential equations of first order. III
• A fixed point approach to the stability of differential equations \(y'=F(x,y)\)
• ON THE HYERS-ULAM-RASSIAS STABILITY OF JENSEN'S EQUATION
• A fixed point theorem of the alternative, for contractions on a generalized complete metric space
• On the Stability of the Linear Functional Equation
• Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions
• Stochastic differential equations. An introduction with applications.