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

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.

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

Complexity ◽  
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.

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

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.

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

2006 ◽  
Vol 06 (03) ◽  
pp. 329-340 ◽  
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.

scholarly journals Fuzzy stochastic differential equations driven by fractional Brownian motion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Marek T. Malinowski ◽  
M. J. Ebadi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Approximation Method ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Stochastic Integral ◽  
Long Range Dependence ◽  
World Systems

AbstractIn this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients.

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