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.     

非齐次隐马尔可夫模型随机变换的若干强极限定理

利用鞅方法讨论了非齐次隐马尔可夫模型变换的强极限定理,作为特殊情形,将随机选择的概念拓展到非齐次隐马尔可夫模型中,得到了关于有限非齐次隐马尔可夫模型随机选择与随机公平比的若干极限定理.     

NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

§1.IntroductionLet(?,F)be a measurable space and let Lb(F)be the space of F-measurable andbounded real functions.A nonlinear expectation is a continuous functionalE[·]:Lb(F)?→Rthat is order preserving(i.e.,E[X1]≥E[X2],if X1≥X2)and constant preserving     

马尔可夫过程穿越次数估计

本文研究了马尔可夫过程穿越次数估计.应用马尔可夫过程向前向后鞅分解方法,得到了穿越次数估计以及Meyer-Zheng拓朴的紧性判别准则,推广了Lyons-Zheng的结果.     

Approximation by walsh-kaczmarz-fejér means on the hardy space

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

On the martingale and free-boundary approaches in sequential detection problems with exponential penalty for delay

We study the connection between the martingale and free-boundary approaches in sequential detection problems for the drift of a Brownian motion, under the assumption of exponential penalty for the delay. By means of the solution of a suitable free-boundary problem, we show that the reward process can be decomposed into the product between a gain function of the boundary point and a positive martingale inside the continuation region.     

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.     

Statistical causality,martingale problems and local uniqueness

The paper considers a statistical concept of causality in continuous time in the filtered probability spaces which is based on the Granger’s definition of causality. The given causality concept is then applied to the solution of the martingale problem (associated with the stochastic differential equation driven with semimartingales). More precisely, we show that the given causality concept is closely connected to the concept of extremality of measures for the solutions of the martingale problem, for the stopped martingale problem and for the local martingale problem. We also show the equivalence between some models of causality and local uniqueness (for the solutions of the martingale problem).