Averaging Principle for Caputo Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Delays

Complexity ◽

10.1155/2021/6646843 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Pengju Duan ◽

Hao Li ◽

Jie Li ◽

Pei Zhang

Keyword(s):

Differential Equation ◽

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equation ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Averaging Principle ◽

Fractional Stochastic Differential Equations

In this article, we investigate a class of Caputo fractional stochastic differential equations driven by fractional Brownian motion with delays. Under some novel assumptions, the averaging principle of the system is obtained. Finally, we give an example to show that the solution of Caputo fractional stochastic differential equations driven by fractional Brownian motion with delays converges to the corresponding averaged stochastic differential equation.

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An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations

Journal of Mathematics ◽

10.1155/2021/8742330 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Weifeng Wang ◽

Lei Yan ◽

Junhao Hu ◽

Zhongkai Guo

Keyword(s):

Differential Equation ◽

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equation ◽

Stochastic Differential Equations ◽

Averaging Principle ◽

Convergence Results ◽

Fractional Stochastic Differential Equations

In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion. Compared with the classic averaging condition for stochastic differential equation, we propose a new averaging condition and obtain the averaging convergence results for Mckean–Vlasov-type Caputo fractional stochastic differential equations.

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Nonparametric estimation of trend for stochastic differential equations driven by sub-fractional Brownian motion

Random Operators and Stochastic Equations ◽

10.1515/rose-2020-2032 ◽

2020 ◽

Vol 28 (2) ◽

pp. 113-122

Author(s):

B. L. S. Prakasa Rao

Keyword(s):

Differential Equation ◽

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equation ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Nonparametric Estimation ◽

Small Noise ◽

Trend Coefficient

AbstractWe discuss nonparametric estimation of a trend coefficient in models governed by a stochastic differential equation driven by a sub-fractional Brownian motion with small noise.

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Existence and Stability of Solutions of Fuzzy Fractional Stochastic Differential Equations with Fractional Brownian Motions

Advances in Fuzzy Systems ◽

10.1155/2021/3948493 ◽

2021 ◽

Vol 2021 ◽

pp. 1-9

Author(s):

Elhoussain Arhrrabi ◽

M’hamed Elomari ◽

Said Melliani ◽

Lalla Saadia Chadli

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Exponential Stability ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Stability Of Solutions ◽

Brownian Motions ◽

Fractional Brownian Motions ◽

Existence And Stability ◽

Fractional Stochastic Differential Equations

The existence, uniqueness, and stability of solutions to fuzzy fractional stochastic differential equations (FFSDEs) driven by a fractional Brownian motion (fBm) with the Lipschitzian condition are investigated. Finally, we investigate the exponential stability of solutions.

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Sobolev-type Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion with Non-Lipschitz Coefficients

Journal of Partial Differential Equations ◽

10.4208/jpde.v32.n2.4 ◽

2019 ◽

Vol 32 (2) ◽

pp. 144-155

Author(s):

Wentao Zhan and Zhi Li sci

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Sobolev Type ◽

Fractional Stochastic Differential Equations

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Approximate Controllability of Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion

Bulletin of the Malaysian Mathematical Sciences Society ◽

10.1007/s40840-019-00825-6 ◽

2019 ◽

Vol 43 (3) ◽

pp. 2605-2626

Author(s):

Jingyun Lv ◽

Xiaoyuan Yang

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Approximate Controllability ◽

Fractional Stochastic Differential Equations

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Non-instantaneous impulsive Hilfer fractional stochastic differential equations driven by fractional Brownian motion

Stochastic Analysis and Applications ◽

10.1080/07362994.2020.1815545 ◽

2020 ◽

pp. 1-18

Author(s):

S. Saravanakumar ◽

P. Balasubramaniam

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Fractional Stochastic Differential Equations

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Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Entropy ◽

10.3390/e20010063 ◽

2018 ◽

Vol 20 (1) ◽

pp. 63 ◽

Cited By ~ 8

Author(s):

Xiao-Li Ding ◽

Juan Nieto

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Analytical Solutions ◽

Time Scale ◽

Fractional Stochastic Differential Equations

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Approximate controllability of fractional stochastic differential equations driven by mixed fractional Brownian motion via resolvent operators

International Journal of Control ◽

10.1080/00207179.2016.1219070 ◽

2016 ◽

Vol 90 (8) ◽

pp. 1713-1727 ◽

Cited By ~ 27

Author(s):

P. Tamilalagan ◽

P. Balasubramaniam

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Approximate Controllability ◽

Resolvent Operators ◽

Mixed Fractional Brownian Motion ◽

Fractional Stochastic Differential Equations

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Exact Null Controllability of Sobolev-Type Hilfer Fractional Stochastic Differential Equations with Fractional Brownian Motion and Poisson Jumps

Bulletin of the Iranian Mathematical Society ◽

10.1007/s41980-018-0043-8 ◽

2018 ◽

Vol 44 (3) ◽

pp. 673-690 ◽

Cited By ~ 7

Author(s):

Hamdy M. Ahmed ◽

JinRong Wang

Keyword(s):

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Fractional Brownian Motion ◽

Null Controllability ◽

Sobolev Type ◽

Poisson Jumps ◽

Fractional Stochastic Differential Equations ◽

Exact Null Controllability

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NON-LIPSCHITZ STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY MULTI-PARAMETER BROWNIAN MOTIONS

Stochastics and Dynamics ◽

10.1142/s021949370600175x ◽

2006 ◽

Vol 06 (03) ◽

pp. 329-340 ◽

Cited By ~ 10

Author(s):

XICHENG ZHANG ◽

JINGYANG ZHU

Keyword(s):

Differential Equation ◽

Brownian Motion ◽

Differential Equations ◽

Stochastic Differential Equation ◽

Stochastic Differential Equations ◽

Lebesgue Measure ◽

Successive Approximation ◽

Existence And Uniqueness ◽

Uniqueness Of Solution ◽

Gronwall’S Inequality

By proving an extension of nonlinear Bihari's inequality (including Gronwall's inequality) to multi-parameter and non-Lebesgue measure, in this paper we first prove by successive approximation the existence and uniqueness of solution of stochastic differential equation with non-Lipschitz coefficients and driven by multi-parameter Brownian motion. Then we study two discretizing schemes for this type of equation, and obtain their L2-convergence speeds.

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