LOCAL TIME ANALYSIS OF ADDITIVE LVY PROCESSES WITH DIFFERENT LVY EXPONENTS

Let X1 XN be independent, classical Levy processes on R^d with Levy exponents ψ1,…, ψN, respectively. The corresponding additive Levy process is defined as the following N-parameter random field on R^d, X（t） △= X1（t1） ＋ ... ＋ XN（tN）, At∈N. Under mild regularity conditions on the ψi＇s, we derive estimate for the local and uniform moduli of continuity of local times of X = {X（t）; t ∈R^N}.

Improved Responses with Multitaper Spectral Analysis for Magnetotelluric Time Series Data Processing:Examples from Field Data

In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without a multitaper approach for spectral estimation.There are several common ways to increase the reliability of the Fourier spectral estimation from experimental(noisy)data;for example to subdivide the experimental time series into segments,taper these segments(using single taper),perform the Fourier transform of the individual segments,and average the resulting spectra.

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

Wind power time series simulation model based on typical daily output processes and Markov algorithm

The simulation of wind power time series is a key process in renewable power allocation planning,operation mode calculation,and safety assessment.Traditional single-point modeling methods discretely generate wind power at each moment;however,they ignore the daily output characteristics and are unable to consider both modeling accuracy and efficiency.To resolve this problem,a wind power time series simulation model based on typical daily output processes and Markov algorithm is proposed.First,a typical daily output process classification method based on time series similarity and modified K-means clustering algorithm is presented.Second,considering the typical daily output processes as status variables,a wind power time series simulation model based on Markov algorithm is constructed.Finally,a case is analyzed based on the measured data of a wind farm in China.The proposed model is then compared with traditional methods to verify its effectiveness and applicability.The comparison results indicate that the statistical characteristics,probability distributions,and autocorrelation characteristics of the wind power time series generated by the proposed model are better than those of the traditional methods.Moreover,modeling efficiency considerably improves.

LÉVY AREA ANALYSIS AND PARAMETER ESTIMATION FOR FOU PROCESSES VIA NON-GEOMETRIC ROUGH PATH THEORY

This paper addresses the estimation problem of an unknown drift parameter matrix for a fractional Ornstein-Uhlenbeck process in a multi-dimensional setting.To tackle this problem,we propose a novel approach based on rough path theory that allows us to construct pathwise rough path estimators from both continuous and discrete observations of a single path.Our approach is particularly suitable for high-frequency data.To formulate the parameter estimators,we introduce a theory of pathwise Itôintegrals with respect to fractional Brownian motion.By establishing the regularity of fractional Ornstein-Uhlenbeck processes and analyzing the long-term behavior of the associated Lévy area processes,we demonstrate that our estimators are strongly consistent and pathwise stable.Our findings offer a new perspective on estimating the drift parameter matrix for fractional Ornstein-Uhlenbeck processes in multi-dimensional settings,and may have practical implications for fields including finance,economics,and engineering.

MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

REPRESENTATION OF ADDITIVE FUNCTIONALS AND LOCAL TIMES FOR JUMP MARKOV PROCESSES AND THEIR FUNCTIONAL LIMIT THEOREM

The representation of additive functionals and local times for jump Markov processes are obtained. The results of uniformly functional moderate deviation and their applications to birth-death processes are also presented.

ABSOLUTE CONTINUITY OF THE OCCUPATION TIME PROCESSES WITH RESPECT TO LEBESGUE MEASURE FOR SUPER－BROWNIAN MOTION

Some properties of Super-Brownian motion have been approached by Dawson & Hochberg [1], Iscoe [2] & L3], Konno & Shiga [4] and so on. In this paper, we limit our attention to the occupation time processes of the Super-Brownian motion,and try to give an intuitive proof for their absolute continuity with respect to the Lebesgue measure on Rd (d≤3) when the initial measure of the Super-Brownian motion has the absolute continuity.

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.

Modeling and Design of Real-Time Pricing Systems Based on Markov Decision Processes

A real-time pricing system of electricity is a system that charges different electricity prices for different hours of the day and for different days, and is effective for reducing the peak and flattening the load curve. In this paper, using a Markov decision process (MDP), we propose a modeling method and an optimal control method for real-time pricing systems. First, the outline of real-time pricing systems is explained. Next, a model of a set of customers is derived as a multi-agent MDP. Furthermore, the optimal control problem is formulated, and is reduced to a quadratic programming problem. Finally, a numerical simulation is presented.

Short and Long-Term Time Series Forecasting Stochastic Analysis for Slow Dynamic Processes

This paper intends to develop suitable methods to provide likely scenarios in order to support decision making for slow dynamic processes such as the underlying of agribusiness. A new method to analyze the short- and long-term time series forecast and to model the behavior of the underlying process using nonlinear artificial neural networks (ANN) is presented. The algorithm can effectively forecast the time-series data by stochastic analysis (Monte Carlo) of its future behavior using fractional Gaussian noise (fGn). The algorithm was used to forecast country risk time series for several countries, both for short term that is 30 days ahead and long term 350 days ahead scenarios.

ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES

Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.

Multiple time scales of fluvial processes—theory and applications

Fluvial processes comprise water flow,sediment transport and bed evolution,which normally feature distinct time scales.The time scales of sediment transport and bed deformation relative to the flow essentially measure how fast sediment transport adapts to capacity region in line with local flow scenario and the bed deforms in comparison with the flow,which literally dictates if a capacity based and/or decoupled model is justified.This paper synthesizes the recently developed multiscale theory for sediment-laden flows over erodible bed,with bed load and suspended load transport,respectively.It is unravelled that bed load transport can adapt to capacity sufficiently rapidly even under highly unsteady flows and thus a capacity model is mostly applicable,whereas a non-capacity model is critical for suspended sediment because of the lower rate of adaptation to capacity.Physically coupled modelling is critical for fluvial processes characterized by rapid bed variation.Applications are outlined on very active bed load sediment transported by flash floods and landslide dam break floods.

A unified approach of PID controller design for unstable processes with time delay

This paper addresses a unified approach of the PID controller design for low as well as high order unstable processes with time delay.The design method is based on the direct synthesis(DS)approach to achieve the enhanced load disturbance rejection.To improve the servo response,a two-degree of freedom control scheme has been considered.A suitable guideline has been provided to select the desired reference model in the DS scheme.The direct synthesis controller has been approximated to the PID controller using the frequency response matching method.A consistently better performance has been obtained in comparison with the recently reported methods.

Remaining Time Prediction for Business Processes with Concurrency Based on Log Representation

Remaining time prediction of business processes plays an important role in resource scheduling and plan making.The structural features of single process instance and the concurrent running of multiple process instances are the main factors that affect the accuracy of the remaining time prediction.Existing prediction methods does not take full advantage of these two aspects into consideration.To address this issue,a new prediction method based on trace representation is proposed.More specifically,we first associate the prefix set generated by the event log to different states of the transition system,and encode the structural features of the prefixes in the state.Then,an annotation containing the feature representation for the prefix and the corresponding remaining time are added to each state to obtain an extended transition system.Next,states in the extended transition system are partitioned by the different lengths of the states,which considers concurrency among multiple process instances.Finally,the long short-term memory(LSTM)deep recurrent neural networks are applied to each partition for predicting the remaining time of new running instances.By extensive experimental evaluation using synthetic event logs and reallife event logs,we show that the proposed method outperforms existing baseline methods.

PID Controller Stabilization for First-order Integral Processes with Time Delay

Due to the widespread application of the PID controller in industrial control systems, it is desirable to know the complete set of all the stabilizing PID controllers for a given plant before the controller design and tuning. In this paper, the stabilization problems of the classical proportionalintegral-derivative （PID） controller and the singleparameter PID controller （containing only one adjustable parameter） for integral processes with time delay are investigated, respectively. The complete set of stabilizing parameters of the classical PID controller is determined using a version of the Hermite-Biehler Theorem applicable to quasipolynomials. Since the stabilization problem of the singie-parameter PID controller cannot be treated by the Hermite-Biehler Theorem, a simple method called duallocus diagram is employed to derive the stabilizing range of the single-parameter PID controller. These results provide insight into the tuning of the PID controllers.

Variance minimization for continuous-time Markov decision processes: two approaches

This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.

Robust H-infinity control of uncertain stochastic time-delay linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper.First,sufficient conditions are proposed in terms of stochastic Lyapunov stability theory,It o differential rule and linear matrix inequality technology.The corresponding controller design is then cast into a convex optimization problem.Attention is focused on constructing an admissible controller,which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals.A numerical example illustrates the effectiveness of the proposed design scheme.

Variance Optimization for Continuous-Time Markov Decision Processes

This paper considers the variance optimization problem of average reward in continuous-time Markov decision process (MDP). It is assumed that the state space is countable and the action space is Borel measurable space. The main purpose of this paper is to find the policy with the minimal variance in the deterministic stationary policy space. Unlike the traditional Markov decision process, the cost function in the variance criterion will be affected by future actions. To this end, we convert the variance minimization problem into a standard (MDP) by introducing a concept called pseudo-variance. Further, by giving the policy iterative algorithm of pseudo-variance optimization problem, the optimal policy of the original variance optimization problem is derived, and a sufficient condition for the variance optimal policy is given. Finally, we use an example to illustrate the conclusion of this paper.

Evolutionary game dynamics of combining the Moran and imitation processes

One of the assumptions of previous research in evolutionary game dynamics is that individuals use only one rule to update their strategy. In reality, an individual's strategy update rules may change with the environment, and it is possible for an individual to use two or more rules to update their strategy. We consider the case where an individual updates strategies based on the Moran and imitation processes, and establish mixed stochastic evolutionary game dynamics by combining both processes. Our aim is to study how individuals change strategies based on two update rules and how this affects evolutionary game dynamics. We obtain an analytic expression and properties of the fixation probability and fixation times(the unconditional fixation time or conditional average fixation time) associated with our proposed process. We find unexpected results. The fixation probability within the proposed model is independent of the probabilities that the individual adopts the imitation rule update strategy. This implies that the fixation probability within the proposed model is equal to that from the Moran and imitation processes. The one-third rule holds in the proposed mixed model. However, under weak selection, the fixation times are different from those of the Moran and imitation processes because it is connected with the probability that individuals adopt an imitation update rule. Numerical examples are presented to illustrate the relationships between fixation times and the probability that an individual adopts the imitation update rule, as well as between fixation times and selection intensity. From the simulated analysis, we find that the fixation time for a mixed process is greater than that of the Moran process, but is less than that of the imitation process. Moreover, the fixation times for a cooperator in the proposed process increase as the probability of adopting an imitation update increases; however, the relationship becomes more complex than a linear relationship.