ON COLLISION LOCAL TIME OF TWO INDEPENDENT FRACTIONAL ORNSTEIN-UHLENBECK PROCESSES

In this article, we study the existence of collision local time of two indepen- dent d-dimensional fractional Ornstein-Uhlenbeck processes X＋^H1 and Xt^H2 with different parameters Hi ∈ （0, 1）,i = 1, 2. Under the canonical framework of white noise analysis, we characterize the collision local time as a Hida distribution and obtain its＇ chaos expansion. Key words Collision local time; fractional Ornstein-Uhlenbeck processes; generalized white noise functionals; choas expansion

Research Progress of the Algebraic and Geometric Signal Processing

The investigation of novel signal processing tools is one of the hottest research topics in modern signal processing community. Among them, the algebraic and geometric signal processing methods are the most powerful tools for the representation of the classical signal processing method. In this paper, we provide an overview of recent contributions to the algebraic and geometric signal processing. Specifically, the paper focuses on the mathematical structures behind the signal processing by emphasizing the algebraic and geometric structure of signal processing. The two major topics are discussed. First, the classical signal processing concepts are related to the algebraic structures, and the recent results associated with the algebraic signal processing theory are introduced. Second, the recent progress of the geometric signal and information processing representations associated with the geometric structure are discussed. From these discussions, it is concluded that the research on the algebraic and geometric structure of signal processing can help the researchers to understand the signal processing tools deeply, and also help us to find novel signal processing methods in signal processing community. Its practical applications are expected to grow significantly in years to come, given that the algebraic and geometric structure of signal processing offer many advantages over the traditional signal processing.

A GENERAL FORM OF THE INCREMENTS OF TWO-PARAMETER FRACTIONAL WIENER PROCESS

A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.

Fractional Processing Based Adaptive Beamforming Algorithm

Fractional order algorithms have shown promising results in various signal processing applications due to their ability to improve performance without significantly increasing complexity.The goal of this work is to inves-tigate the use of fractional order algorithm in the field of adaptive beam-forming,with a focus on improving performance while keeping complexity lower.The effectiveness of the algorithm will be studied and evaluated in this context.In this paper,a fractional order least mean square(FLMS)algorithm is proposed for adaptive beamforming in wireless applications for effective utilization of resources.This algorithm aims to improve upon existing beam-forming algorithms,which are inefficient in performance,by offering faster convergence,better accuracy,and comparable computational complexity.The FLMS algorithm uses fractional order gradient in addition to the standard ordered gradient in weight adaptation.The derivation of the algorithm is provided and supported by mathematical convergence analysis.Performance is evaluated through simulations using mean square error(MSE)minimization as a metric and compared with the standard LMS algorithm for various parameters.The results,obtained through Matlab simulations,show that the FLMS algorithm outperforms the standard LMS in terms of convergence speed,beampattern accuracy and scatter plots.FLMS outperforms LMS in terms of convergence speed by 34%.From this,it can be concluded that FLMS is a better candidate for adaptive beamforming and other signal processing applications.

Existence and joint continuity of local time of multi-parameter fractional Lévy processes

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

Boron isotope geochemistry of Bangor Co Salt Lake(central Tibet):implications for boron origin and uneven mixing of lake water

Boron is an essential,widely used,micronutrient element and is abundant in salt lakes on the Qinghai-Tibet Plateau.The origin and distribution of boron brine deposits on the Qinghai-Tibet Plateau is an important foundation for B resource formation,evolution,and enrichment,which have long been the subject of debate.The boron isotope system is a sensitive geochemical tracer,making it useful for eff ectively and precisely tracking a wide range of geological processes and sources.This study investigates the major cations,[B],andδB values of samples(lake brine,river waters,and cold spring water)from the Bangor Co Lake which is a typical salt lake rich in boron in Tibet,China.There are magnitude-scale diff erences in[B]among diff erent sample types:river samples<cold spring water<<brine lakes.[B]values vary from 0.73 to~1113 mg/L.Similar to[B],theδB values of the samples exhibit magnitude-scale variations as[B],ranging from-7.35‰to+7.66‰.There are also magnitude-scale diff erences inδB among diff erent sample types.TheδB values of cold spring water are relatively low,and the values range from-1.26‰to-7.75‰.However,the river water samples and saline lakes have higher values,from 0.38‰to 4.62‰,and theδB values of river water samples are basically in the distribution range of those of Bangor Co Lake.This indicates that the sources of boron in Bangor Co Lake are mainly the recharge water with higherδB values and spring water with lowerδB values,and the boron sources and the uneven mixing of lake water are two reasons that account for the large change in theδB value of Bangor Co Lake.

Asymptotics for Nonlinear Transformations of Fractionally Integrated Time Series

The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is diffent from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.

Moderate Deviations for Parameter Estimation in the Fractional Ornstein–Uhlenbeck Processes with Periodic Mean

In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviations,as well as the moderation deviation principle with explicit rate function can be obtained.

On large increments of a two-parameter fractional Wiener process

In this paper, how big the increments are and some liminf behaviors are studied of a two-parameter fractional Wiener process. The results are based on some inequalities on the suprema of this process, which also are of independent interest.

Least squares estimator of Ornstein-Uhlenbeck processes driven by fractional Levy processes with periodic mean

VVc deal with the least squares estimator for the drift parameters of an Ornstein-Uhlenbeck process with periodic mean function driven by fractional Levy process.For this estimator,we obtain consistency and the asymptotic distribution.Compared with fractional Ornstein-Uhlenbeck and Ornstein-Uhlenbeck driven by Levy process,they can be regarded both as a Levy generalization of fractional Brownian motion and a fractional generalization of Levy process.

The invariance principle for fractionally integrated processes with strong near-epoch dependent innovations

In this paper, we show the invariance principle for the partial sum processes of fractionally integrated processes, otherwise known as I(d + m) processes, where |d| < 1/2 and m is a nonnegative integer, with strong near-epoch dependent innovations. The results are applied to the test of unit root. The conditions given improve previous results in the literature concerning fractionally integrated processes.

A Liminf Result on Two-parameter Gaussian Process

Abstract In this paper, a liminf behavior is studied of a two-parameter Gaussian process which is a generalization of a two-parameter Wiener process. The results improve on the liminfs in [7].

Performance Modeling for Data Monitoring Services in Smart Grid: A Network Calculus Based Approach

This paper focuses on solving the modeling issues of monitoring system service performance based on the network calculus theory.First,we formulate the service model of the smart grid monitoring system.Then,we derive the flow arrival curve based on the incremental process related functions.Next,we develop flow arrival curves for the case of the incremental process being a fractional Gaussian process,and then we obtain the generalized Cauchy process.Three technical theorems related to network calculus are presented as our main results.Mathematically,the variance of arrival flow for the continuous time case is derived.Assuming that the incremental process of network flow is a Gaussian stationary process,and given the auto-correlation function of the incremental process with violation probability,the formula of the arrival curve is derived.In addition,the overall flow variance under the discrete time case is explicitly derived.The theoretical results are evaluated in smart grid applications.Simulations indicate that the generalized Cauchy process outperforms the fractional Gaussian process for our considered problem.

Parameter Estimation for the Discretely Observed Vasicek Model with Small Fractional Lévy Noise

The statistical inference of the Vasicek model driven by small Levy process has a long history.In this paper,we consider the problem of parameter estimation for Vasicek model dX_t=(μ-θX_t)dt+εdL_t^d,t∈[0,1],X_0=x_0,driven by small fractional Lévy noise with the known parameter d less than one half,based on discrete high-frequency observations at regularly spaced time points{t_i=i/n,i=1,2,...,n}.For the general case and the null recurrent case,the consistency as well as the asymptotic behavior of least squares estimation of unknown parametersμandθhave been established as small dispersion coefficientε→0 and large sample size n→∞simultaneously.

Next generation of power electronic-converter application for energy-conversion and storage units and systems

By a rearrangement of the traditional supply-converter-load system connection,partial-power-processing-based converters can be used to achieve a reduction in size and cost,increase in system efficiency and lower device power rating.The concept is promising for different applications such as photovoltaic arrays,electric vehicles and electrolysis.For photovoltaic applications,it can drive each cell in the array to its maximum power point with a relatively smaller converter;for electric-vehicle applications,both an onboard charger with reduced weight and improved efficiency as well as a fast charger station handling higher power can be considered.By showing different examples of partial-power-processing application for energy-conversion and storage units and systems,this paper discusses key limitations of partial-power-processing and related improvements from different perspectives to show the potential in future power electronic systems.

Parisian ruin over a finite-time horizon

For a risk process R_u(t) = u + ct- X(t), t≥0, where u≥0 is the initial capital, c > 0 is the premium rate and X(t), t≥0 is an aggregate claim process, we investigate the probability of the Parisian ruin P_S(u, T_u) = P{inf (t∈[0,S]_(s∈[t,t+T_u])) sup R_u(s) < 0}, S, T_u > 0.For X being a general Gaussian process we derive approximations of P_S(u, T_u) as u →∞. As a by-product, we obtain the tail asymptotic behaviour of the infimum of a standard Brownian motion with drift over a finite-time interval.

On Global and Local Properties of the Trajectories of Gaussian Random Fields——A Look Through the Set of Limit Points

This paper studies the global and local properties of the trajectories of Gaussian random fields with stationary increments and proves sufficient conditions for Strassen's functional laws of the iterated logarithm at zero and infinity respectively.The sets of limit points of those Gaussian random fields are obtained.The main results are applied to fractional Riesz-Bessel processes and the sets of limit points of this field are obtained.

A model for expansion ratio in liquid-solid fluidized beds

Liquid-solid fluidized beds are used in mineral processing industries to separate particles based on parti- cle size, density, and shape. Understanding the expanded fluidized bed is vital for accurately assessing its performance. Expansion characteristics of the fluidized bed were studied by performing several experi- ments with iron ore, chromite, quartz, and coal samples. Using water as liquid medium, experiments were conducted to study the effects of particle size, particle density, and superficial velocity on fluidized bed expansion. The experimental data were utilized to develop an empirical mathematical model based on dimensional analysis to estimate the expansion ratio of the fluidized bed in terms of particle character- istics, operating and design parameters. The predicted expansion ratio obtained from the mathematical model is in good agreement with the experimental data.