Parametric inference for stochastic differential equations driven by a mixed fractional Brownian motion with random effects based on discrete observations

2021 ◽  
pp. 1-12
Author(s):  
B.L.S. Prakasa Rao
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Random Effects ◽  
Parametric Inference ◽  
Discrete Observations ◽  
Mixed Fractional Brownian Motion

scholarly journals Parameter Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Na Song ◽  
Zaiming Liu
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Asymptotic Properties ◽  
Regularity Conditions ◽  
Minimum Distance Estimator ◽  
Mixed Fractional Brownian Motion ◽  
Distance Estimator ◽  
Drift Parameter

We study the asymptotic properties of minimum distance estimator of drift parameter for a class of nonlinear scalar stochastic differential equations driven by mixed fractional Brownian motion. The consistency and limit distribution of this estimator are established as the diffusion coefficient tends to zero under some regularity conditions.

scholarly journals Existence and exponential stability in the pth moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Shouming Zhong
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Banach Fixed Point Theorem ◽  
Mixed Fractional Brownian Motion

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

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