PRELIMINARY STUDY OF BAROTROPIC STOCHASTIC DIFFERENCE MODEL APPLIED TO WEATHER PREDICTION

In order to consider both the deterministic and the stochastic property of atmospheric motion simul- taneously,in this paper,the weather prediction is proposed as the problem of the evolution of meteorological field.The historical viewpoint of atmospheric motion is emphasized here.Based on time series analysis te- chnique,a stochastic-dynamical model with multiple initial fields is derived.Thus,weather forecasting is sum- meal up as a problem of solving a set of stochastic difference equations.For the barotropic atmosphere,the numerical solutions of the equations are obtained by using the method of empirical orthogonal functions (EOF),and examples of medium-range weather prediction are given here.Meanwhile,selecting the order of time series,i.e.,determining the number of initial fields properly,is also discussed.

Decentralized Optimal Control and Stabilization of Interconnected Systems With Asymmetric Information

The paper addresses the decentralized optimal control and stabilization problems for interconnected systems subject to asymmetric information.Compared with previous work,a closed-loop optimal solution to the control problem and sufficient and necessary conditions for the stabilization problem of the interconnected systems are given for the first time.The main challenge lies in three aspects:Firstly,the asymmetric information results in coupling between control and estimation and failure of the separation principle.Secondly,two extra unknown variables are generated by asymmetric information(different information filtration)when solving forward-backward stochastic difference equations.Thirdly,the existence of additive noise makes the study of mean-square boundedness an obstacle.The adopted technique is proving and assuming the linear form of controllers and establishing the equivalence between the two systems with and without additive noise.A dual-motor parallel drive system is presented to demonstrate the validity of the proposed algorithm.

THE LONG TIME BEHAVIOR OF THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS WITH LINEAR SELF-REPELLING DRIFT

Let B^(H) be a fractional Brownian motion with Hurst index 1/2≤H<1.In this paper,we consider the equation(called the Ornstein-Uhlenbeck process with a linear self-repelling drift)dX_(t)^(H)=dB_(t)^(H)+σ X_(t)^(H)dt+vdt-θ(∫_(0)^(t)(X_(t)^(H)-X_(s)^(H))ds)dt,whereθ<0,σ,v∈ℝ.The process is an analogue of self-attracting diffusion(Cranston,Le Jan.Math Ann,1995,303:87–93).Our main aim is to study the large time behaviors of the process.We show that the solution X^(H)diverges to infinity as t tends to infinity,and obtain the speed at which the process X^(H)diverges to infinity.

Time-Inconsistent Stochastic LQ Problem with Regime Switching

This paper investigates a time-inconsistent stochastic linear-quadratic problem with regime switching that is characterized via a finite-state Markov chain.Open-loop equilibrium control is studied in this paper whose existence is characterized via Markov-chain-modulated forward-backward stochastic difference equations and generalized Riccati-like equations with jumps.

ANALYSIS OF MULTI-INDEX MONTE CARLO ESTIMATORS FOR A ZAKAI SPDE

In this article, we propose a space-time Multi-Index Monte Carlo （MIMC） estimator for a one-dimensional parabolic stochastic partial differential equation （SPDE） of Zakai type. We compare the complexity with the Multilevel Monte Carlo （MLMC） method of Giles and Reisinger （2012）, and find, by means of Fourier analysis, that the MIMC method： （i） has suboptimal complexity of 0（ε^-21 ｜ogε｜） for a root mean square error （RMSE） z if the same spatial discretisation as in the MLMC method is used; （ii） has a better complexity of 0（ε^-21 ｜ogε｜） if a carefully adapted discretisation is used; （iii） has to be adapted for non-smooth functionals. Numerical tests confirm these findings empirically.