An averaging principle for stochastic differential equations of fractional order 0 < α < 1
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Wenjing Xu
und
Kai Lu
Abstract
This paper presents an averaging principle for fractional stochastic differential equations in ℝn with fractional order 0 < α < 1. We obtain a time-averaged equation under suitable conditions, such that the solutions to original fractional equation can be approximated by solutions to simpler averaged equation. By mathematical manipulations, we show that the mild solution of two equations before and after averaging are equivalent in the sense of mean square, which means the classical Khasminskii approach for the integer order systems can be extended to fractional systems.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 11872305, 11532011) and China Scholarship Council (No.201906290182).
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© 2020 Diogenes Co., Sofia
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 23–3–2020)
- Survey Paper
- Why fractional derivatives with nonsingular kernels should not be used
- Fractional-order susceptible-infected model: Definition and applications to the study of COVID-19 main protease
- Generalized fractional Poisson process and related stochastic dynamics
- Research Paper
- Determination of the fractional order in semilinear subdiffusion equations
- Degenerate Kirchhoff (p, q)–Fractional systems with critical nonlinearities
- Solution of linear fractional order systems with variable coefficients
- “Fuzzy” calculus: The link between quantum mechanics and discrete fractional operators
- The green function for a class of Caputo fractional differential equations with a convection term
- Inverse problem for a multi-term fractional differential equation
- Maximum principles for a class of generalized time-fractional diffusion equations
- Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method
- Variational approximation for fractional Sturm–Liouville problem
- The 2-adic derivatives and fractal dimension of Takagi-like function on 2-series field
- Construction of fixed point operators for nonlinear difference equations of non integer order with impulses
- An averaging principle for stochastic differential equations of fractional order 0 < α < 1
- Weak solvability of the variable-order subdiffusion equation
Artikel in diesem Heft
- Frontmatter
- Editorial Note
- FCAA related news, events and books (FCAA–Volume 23–3–2020)
- Survey Paper
- Why fractional derivatives with nonsingular kernels should not be used
- Fractional-order susceptible-infected model: Definition and applications to the study of COVID-19 main protease
- Generalized fractional Poisson process and related stochastic dynamics
- Research Paper
- Determination of the fractional order in semilinear subdiffusion equations
- Degenerate Kirchhoff (p, q)–Fractional systems with critical nonlinearities
- Solution of linear fractional order systems with variable coefficients
- “Fuzzy” calculus: The link between quantum mechanics and discrete fractional operators
- The green function for a class of Caputo fractional differential equations with a convection term
- Inverse problem for a multi-term fractional differential equation
- Maximum principles for a class of generalized time-fractional diffusion equations
- Multiple positive solutions for a nonlocal PDE with critical Sobolev-Hardy and singular nonlinearities via perturbation method
- Variational approximation for fractional Sturm–Liouville problem
- The 2-adic derivatives and fractal dimension of Takagi-like function on 2-series field
- Construction of fixed point operators for nonlinear difference equations of non integer order with impulses
- An averaging principle for stochastic differential equations of fractional order 0 < α < 1
- Weak solvability of the variable-order subdiffusion equation
