A version of Burkholder's theorem for operator-weighted spaces

Let be an operator weight, i.e. a weight function taking values in the bounded linear operators on a Hilbert space . We prove that if the dyadic martingale transforms are uniformly bounded on for each dyadic grid in , then the Hilbert transform is bounded on as well, thus providing an analogue of Burkholder's theorem for operator-weighted -spaces. We also give a short new proof of Burkholder's theorem itself. Our proof is based on the decomposition of the Hilbert transform into ``dyadic shifts'.

     

Clarkson不等式与Banach空间几何

我们证明了Banach空间X是Clarkson p型（q余型）当且仅当X是一个特殊的p一致光滑空间（q-一致凸空间（）,我们还找到刻划型（余型）的一系列鞅不等式,同时,我们得到了均方函数sharp不等式。     

Diffusion Processes Associated with Nonlinear Evolution Equations for Signed Measures

In this paper, we explain how to associate a nonlinear martingale problem with some nonlinear parabolic evolution equations starting at bounded signed measures. Our approach generalizes the classical link made when the initial condition is a probability measure. It consists in giving to each sample-path a signed weight which depends on the initial position. After dealing with the classical McKean-Vlasov equation as an introductory example, we are interested in a viscous scalar conservation law. We prove uniqueness for the corresponding nonlinear martingale problem and then obtain existence thanks to a propagation of chaos result for a system of weakly interacting diffusion processes. Last, we study the behavior of the associated fluctuations and present numerical results which confirm the theoretical rate of convergence.     

保费收取过程是随机过程的双险种风险模型

研究保费收取过程是一个随机过程的双险种风险模型,得出了Lundberg上界、最终破产概率、不破产所满足的微积分方程、索赔服从指数分布的不破产概率、有限时间不破产所满足的微积分方程.     

跳扩散模型下的欧式障碍期权的定价

本文在标的资产价格服从跳扩散模型的假设下,运用Girsanov定理获得了价格过程的等价鞅测度,用期权定价的鞅方法得出障碍期权的定价公式.     

A new method for estimating bounds of eigenvalues

A new method for estimating the bounds of eigenvalues is presented. In order to show that the method proposed is as effective as Qiu's, an undamping spring-mass system with 5 nodes and 5 degrees of freedom is given. To illustrate that the present method can be applied to structures which cannot be treated by non-negative decomposition, a plane frame with 202 nodes and 357 beam elements is given. The results show that the present method is effective for estimating the bounds of eigenvalues and is more common than Qiu's. Project supported by the National Natural Science Foundation (No. 19872028) and the Mechanical Technology Development Foundation of China.     

受控AR模型中参数估计误差的一致有界性分析

本针对系统为受控AR模型，其参数估计采用随机梯度算法时，用鞅收敛定理的推广形式分析了它的收敛性，得到了参数估计误差一致有界的结果．     

Generalized jump-type Ornstein-Uhlenbeck processes as limits of infinite-particle systems

We prove the existence and uniquencess of the solution to the martingale problem associated with jump-type Ornstein-Uhlenbeck processes in the Schwartz space of distributions onR ^d. An example of a noninteracting infinite-particle system is given, which after rescaling has such a process as a limit. Cases when such a process has an invariant measure are identified.     

汽车保险的广义泊松过程模型

本文针对汽车保险中多车辆相撞事故的理赔建立起广义泊松过程模型,利用概率母泛函给出了其理赔总量在(0,t]内的均值与方差,并基于鞅分析方法证明了其破产概率的Lundberg不等式.     

APPROXIMATION BY WALSH-KACZMARZ-FEJ ′ER MEANS ON THE HARDY SPACE

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.