Mean square exponential stabilization of uncertain time‐delay stochastic systems with fractional Brownian motion

2021 ◽  
Author(s):  
Majid Parvizian ◽  
Khosro Khandani
Keyword(s):  
Brownian Motion ◽  
Time Delay ◽  
Fractional Brownian Motion ◽  
Stochastic Systems ◽  
Exponential Stabilization ◽  
Mean Square ◽  
Uncertain Time

A New Controller of Stochastic Delay Systems

2011 ◽  
Vol 63-64 ◽  
pp. 974-977
Author(s):  
Yun Chen ◽  
Qing Qing Li
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Mean Square ◽  
Closed Loop System ◽  
Stochastic Delay ◽  
Numerical Example ◽  
Mean Square Stability ◽  
Delay Dependent

By introducing an additional vector, a new delay-dependent controller is designed for stochastic systems with time delay in this paper. The presented controller is formulated by means of LMI, and it guarantees robust asymptotical mean-square stability of the resulting closed-loop system. Our result shows advantage over some existing ones, which is demonstrated by a numerical example.

scholarly journals On some statistics of fractional Brownian motion

2021 ◽  
pp. 131-138
Author(s):  
Viktor Bondarenko
Keyword(s):  
Stochastic Process ◽  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Hurst Exponent ◽  
Limit Theorems ◽  
Goodness Of Fit ◽  
Mean Square ◽  
One Step ◽  
Optimal Forecasting

Fractional Brownian motion as a method for estimating the parameters of a stochastic process by variance and one-step increment covariance is proposed and substantiated. The root-mean-square consistency of the constructed estimates has been proven. The obtained results complement and generalize the consequences of limit theorems for fractional Brownian motion, that have been proved in the number of articles. The necessity to estimate the variance is caused by the absence of a base unit of time and the estimation of the covariance allows one to determine the Hurst exponent. The established results let the known limit theorems to be used to construct goodness-of-fit criteria for the hypothesis “the observed time series is a transformation of fractional Brownian motion” and to estimate the error of optimal forecasting for time series.

scholarly journals Distance between the fractional Brownian motion and the space of adapted Gaussian martingales

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Yuliya Mishura ◽  
Sergiy Shklyar
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Fractional Brownian Motion ◽  
Convex Analysis ◽  
Minimax Problem ◽  
Mean Square ◽  
Martingale Representation

We consider the distance between the fractional Brownian motion defined on the interval [0,1] and the space of Gaussian martingales adapted to the same filtration. As the distance between stochastic processes, we take the maximum over [0,1] of mean-square deviances between the values of the processes. The aim is to calculate the function a in the Gaussian martingale representation ∫0ta(s)dWs that minimizes this distance. So, we have the minimax problem that is solved by the methods of convex analysis. Since the minimizing function a can not be either presented analytically or calculated explicitly, we perform discretization of the problem and evaluate the discretized version of the function a numerically.

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