Power load fluctuation is generally agreed to be a non-stationary stochastic process. The Fractional Brownian Motion (FBM) model is proposed to forecast a non-stationary time series with high ...accuracy. Computation of the Hurst exponent (H) for the power load data series using the Rescaled Range Analysis (R/S) in this study. This method is used to verify the Long-Range Dependent (LRD) characteristics of non-stationary power load data. For the real power load, however, H exponent takes on the self-similarity characteristics in a certain finite range of intervals, the global self-similarity is very rare to exist. The H exponent of the self-similarity usually has more than one value. We generalize multifractional H(t) to replace constant H. To improve the forecasting accuracy, the H(t) is optimized by the Quantum-Behaved Particle Swarm Optimization (QPSO). Once the optimal H(t) is obtained, then the optimal and parameters in the multi-Fractional Brownian Motion (mFBM) model can be deduced to forecast next power load data series with a higher accuracy.
•Fractional Brownian Motion (FBM)as Stochastic model forecasts a power load series.•The parameters of the FBM are estimated by R/S and MSE methods.•The parameters of the FBM are optimized by PSO and QPSO.•The prediction errors of RNN,FBM,PSO + FBM,QPSO + FBM were analyzed by using box-plot and norm-plot.
The present article is devoted to discuss the pth moment exponential ultimate boundedness for a class of stochastic distributed delay-coupled systems on networks driven by G-Brownian motion. By ...combining the method of proof by contradiction with Lyapunov method and graph theory, some sufficient condition for both the Lyapunov-type theorem and the coefficients-type theorem are proposed to ensure the pth moment exponential ultimate boundedness of the considered systems. As applications, the boundedness criteria are applied to stochastic distributed delay-coupled neural networks and stochastic distributed delay-coupled control systems in the framework of G-Brownian motion.
Abstract
Diffusion of nanoparticles in the cytoplasm of live cells has frequently been reported to exhibit an anomalous and even heterogeneous character, i.e. particles seem to switch gears during ...their journey. Here we show by means of a hidden Markov model that individual trajectories of quantum dots in the cytoplasm of living cultured cells feature a dichotomous switching between two distinct mobility states with an overall subdiffusive mode of motion of the fractional Brownian motion (FBM) type. Using the extracted features of experimental trajectories as input for simulations of different variants of a two-state FBM model, we show that the trajectory-intrinsic and the ensemble-wise heterogeneity in the experimental data is mostly due to variations in the (local) transport coefficients, with only minor contributions due to locally varying anomaly exponents. Altogether, our approach shows that diffusion heterogeneities can be faithfully extracted and quantified from fairly short trajectories obtained by single-particle tracking in highly complex media.
We study the fluctuations of the area A=∫0Tx(t)dt under a one-dimensional Brownian motion x(t) in a trapping potential ∼|x|, at long times T→∞. We find that typical fluctuations of A follow a ...Gaussian distribution with a variance that grows linearly in time (at large T), as do all higher cumulants of the distribution. However, large deviations of A are not described by the “usual” scaling (i.e., the large deviations principle), and are instead described by two different anomalous scaling behaviors: Moderately-large deviations of A, obey the anomalous scaling PA;T∼e−T1/3fA/T2/3 while very large deviations behave as PA;T∼e−TΨA/T2. We find the associated rate functions f and Ψ exactly. Each of the two functions contains a singularity, which we interpret as dynamical phase transitions of the first and third order, respectively. We uncover the origin of these striking behaviors by characterizing the most likely scenario(s) for the system to reach a given atypical value of A. We extend our analysis by studying the absolute area B=∫0T|x(t)|dt and also by generalizing to higher spatial dimension, focusing on the particular case of three dimensions.
•We uncover two large-deviation regimes, each exhibiting anomalous scaling.•We calculate the associated large-deviation functions (LDFs) exactly.•We uncover singularities in these LDFs, interpreted as dynamical phase transitions.•Despite these anomalous behaviors, typical fluctuations exhibit usual behavior.•We calculate the coefficients of the linear growth of all cumulants in time.
In this paper, we propose a new stochastic epidemic model as follows
where
The model embodies both the mean and variance uncertainty. It can be seen as an extension of the existing model. It shows a ...unique positive solution in the sense of quasi surely and will asymptotically tend to zero quasi surely and is pth-moment stable.
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