AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LéVY NOISE

In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.

AVERAGING PRINCIPLE FOR QUASI-GEOSTROPHIC MOTIONUNDER RAPIDLY OSCILLATING FORCING

A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.

EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.

Multimodal Medical Image Registration and Fusion for Quality Enhancement

For the last two decades,physicians and clinical experts have used a single imaging modality to identify the normal and abnormal structure of the human body.However,most of the time,medical experts are unable to accurately analyze and examine the information from a single imaging modality due to the limited information.To overcome this problem,a multimodal approach is adopted to increase the qualitative and quantitative medical information which helps the doctors to easily diagnose diseases in their early stages.In the proposed method,a Multi-resolution Rigid Registration(MRR)technique is used for multimodal image registration while Discrete Wavelet Transform(DWT)along with Principal Component Averaging(PCAv)is utilized for image fusion.The proposed MRR method provides more accurate results as compared with Single Rigid Registration(SRR),while the proposed DWT-PCAv fusion process adds-on more constructive information with less computational time.The proposed method is tested on CT and MRI brain imaging modalities of the HARVARD dataset.The fusion results of the proposed method are compared with the existing fusion techniques.The quality assessment metrics such as Mutual Information(MI),Normalize Crosscorrelation(NCC)and Feature Mutual Information(FMI)are computed for statistical comparison of the proposed method.The proposed methodology provides more accurate results,better image quality and valuable information for medical diagnoses.

The Averaging Principle for Stochastic Fractional Partial Differential Equations with Fractional Noises

The purpose of this paper is to establish an averaging principle for stochastic fractional partial differential equation of order a.>1 driven by a fractional noise.We prove the existence and uniqueness of the global mild solution for the considered equation by the fixed point principle.The solutions for SPDEs with fractional noises can be approximated by the solution for the averaged stochastic systems in the sense of p-moment under some suitable assumptions.

An Averaging Principle for Caputo Fractional Stochastic Differential Equations with Compensated Poisson Random Measure

This article deals with an averaging principle for Caputo fractional stochastic differential equations with compensated Poisson random measure.The main contribution of this article is impose some new averaging conditions to deal with the averaging principle for Caputo fractional stochastic differential equations.Under these conditions,the solution to a Caputo fractional stochastic differential system can be approximated by that of a corresponding averaging equation in the sense ofmean square.

Stochastic Averaging Principle for Mixed Stochastic Differential Equations

In this paper,an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion,a fractional Brownian motion B^(H) with the Hurst parameter H>1/2 and a discontinuous drift was estimated.Under some proper assumptions,we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the Ito stochastic calculus.

Fast-slow stochastic dynamical system with singular coefficients

This paper aims to study the asymptotic behavior of a fast-slow stochastic dynamical system with singular coefficients,where the fast motion is given by a continuous diffusion process while the slow component is driven by anα-stable noise withα∈[1,2).Using Zvonkin’s transformation and the technique of the Poisson equation,we have that both the strong and weak convergences in the averaging principle are established,which can be viewed as a functional law of large numbers.Then we study the small fluctuations between the original system around its average.We show that the normalized difference converges weakly to an Ornstein-Uhlenbeck type Gaussian process,which is a form of the functional central limit theorem.Furthermore,sharp rates for the above convergences are also obtained,and these convergences are shown to not depend on the regularities of the coefficients with respect to the fast variable,which reflect the effects of noises on the multi-scale systems.