Quenching phenomenon of a time‐fractional diffusion equation with singular source term

In this paper, a time‐fractional diffusion equation with singular source term is considered. The Caputo fractional derivative with order 0<α ?1 is applied to the temporal variable. Under specific initial and boundary conditions, we find that the time‐fractional diffusion equation presents quenching solution that is not globally well‐defined as time goes to infinity. The quenching time is estimated by using the eigenfunction of linear fractional diffusion equation. Moreover, by implementing a finite difference scheme, we give some numerical simulations to demonstrate the theoretical analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

Generalized asymptotic functions in nonconvex multiobjective optimization problems

In this paper, we use generalized asymptotic functions and second-order asymptotic cones to develop a general existence result for the nonemptiness of the proper efficient solution set and a sufficient condition for the domination property in nonconvex multiobjective optimization problems. A new necessary condition for a point to be efficient or weakly efficient solution is given without any convexity assumption. We also provide a finer outer estimate for the asymptotic cone of the weakly efficient solution set in the quasiconvex case. Finally, we apply our results to the linear fractional multiobjective optimization problem.     

Wavelet-based estimator for the hurst parameters of fractional brownian sheet

It is proposed a class of statistical estimators H =(H_1,…,H_d) for the Hurst parameters H =(H_1,…,H_d) of fractional Brownian field via multi-dimensional wavelet analysis and least squares,which are asymptotically normal.These estimators can be used to detect self-similarity and long-range dependence in multi-dimensional signals,which is important in texture classification and improvement of diffusion tensor imaging(DTI) of nuclear magnetic resonance(NMR).Some fractional Brownian sheets will be simulated and the simulated data are used to validate these estimators.We find that when H_i ≥ 1/2,the estimators are accurate,and when H_i 1/2,there are some bias.     

一类1 < α < 2非局部条件下的脉冲分数阶微分方程mild解的存在性

本文研究了一类1 < α < 2非局部条件下的脉冲分数阶偏微分方程mild解的存在性问题.利用解算子的相关性质及Krasnoselskii不动点理论的方法,获得了这类方程的mild解并予以证明,且得到了解的存在性结果.     

分数阶尺度函数的分解与重构算法

引入分数阶多分辨分析与分数阶尺度函数的概念.运用时频分析方法与分数阶小波变换,研究了分数阶正交小波的构造方法,得到分数阶正交小波存在的充要条件.给出分数阶尺度函数与小波的分解与重构算法,算法比经典的尺度函数与小波的分解与重构算法更具有一般性.     

分数扩散模型的参数估计及其应用

研究分数扩散模型的参数估计及其应用问题.分数扩散模型是一类由分数Brownian运动驱动的随机微分方程.主要结果有:(1)利用二次变差方法给出模型中扩散系数的估计量,通过最小二乘法给出模型中漂移系数的估计量;(2)证明这些估计量的一致收敛性和渐近正态性;(3)利用MCMC方法对此估计量进行验证,并通过R软件将上述模型以及参数估计量应用到SHIBOR利率中进行实证研究.     

Generalized harmonic number summation formulae via hypergeometric series and digamma functions

By computing the derivatives of five classical hypergeometric summation theorems, and applying the related properties of the digamma function, we derive a large number of closed summation formulae for generalized harmonic numbers.     

Bounds on partial derivatives of NURBS surfaces

In this paper, we estimate the partial derivative bounds for Non-Uniform Rational B-spline(NURBS) surfaces. Firstly, based on the formula of translating the product into sum of B-spline functions, discrete B-spline theory and Dir function, some derivative bounds on NURBS curves are provided. Then, the derivative bounds on the magnitudes of NURBS surfaces are proposed by regarding a rational surface as the locus of a rational curve. Finally, some numerical examples are provided to elucidate how tight the bounds are.     

Unifying pricing formula for several stochastic volatility models with jumps

In this paper, we introduce a unifying approach to option pricing under continuous‐time stochastic volatility models with jumps. For European style options, a new semi‐closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro‐differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log‐normal and a log‐uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yan and Hanson, respectively. The comparison of existing and newly proposed option pricing formulas with respect to time efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out‐of‐the money contracts. Copyright © 2017 John Wiley & Sons, Ltd.