Stability of Doob—Meyer Decomposition Under Extended Convergence

In what follows, we consider the relation between Aldous‘s extended convergence and weak convergence of filtrations. We prove that, for a sequence (X^n) of Ft^n )-special semimartingales, with canonical decomposition X^n =M^n A^n, if the extended convergence (X^n,F.^n)→(X,T. ) holds with a quasi-left continuous (Ft)-special semimartingale X = M A, then, under an additional assumption of uniform integrability,we get the convergence in probability under the Skorokhod topology: M^n↑P→M and A^n↑P→ A.     

非Lipschitz条件下g 上鞅的非线性Doob Meyer分解

作者讨论非Lipschitz条件下g 上鞅的非线性Doob Meyer 分解.　为此讨论一类漂移系数g(s,·,·)关于(y,z)不满足Lipschitz条 件的倒向随机微分方程解的存在唯一性,运用Biharis不等式证明了一类倒向随机微分方程的比较定理以及g 上解的极限定理.     

Nonlinear Doob-Meyer Decomposition for General Filtration

The comparison theorem for generalized backward stochastic differential equations is discussed. Some topics related to equations of this type are also investigated.     

含非线性源项的变分不等式的加性区域分解法

本文研究一类求解非线性变分不等式的加性区域分解法,其中区域分解为非重叠子区域,在界面上采用Robin条件,得到了算法的收敛性,而且数值算例表明,选取适合的Robin参数可加快算法的收敛速度.     

Analysis of Decomposition Algorithms with Benders Cuts for p-Median Problem

In this paper the algorithms for solving the p-median problem based on the Benders decomposition are investigated. A family of problems hard for solving with such algorithms is constructed and then generalized to a special NP-hard case of the p-median problem. It is shown that the effectiveness of the considered algorithms depends on the choice of the optimal values of the dual variables used in Benders cuts. In particular, the depth of the cuts can be equal to one.     

Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

In this paper, we prove that the weak solutions u∈Wloc^1, p （Ω） （1 〈p〈∞） of the following equation with vanishing mean oscillation coefficients A（x）： -div[（A（x）△↓u·△↓u）p-2/2 A（x）△↓u＋│F（x）│^p-2 F（x）]=B（x, u, △↓u）, belong to Wloc^1, q （Ω）（A↓q∈（p, ∞）, provided F ∈ Lloc^q（Ω） and B（x, u, h） satisfies proper growth conditions where Ω ∪→R^N（N≥2） is a bounded open set, A（x）=（A^ij（x）） N×N is a symmetric matrix function.     

M-Estimation for Discretely Observed Ergodic Diffusion Processes with Infinitely Many Jumps

We study parametric inference for multidimensional stochastic differential equations with jumps from some discrete observations. We consider a case where the structure of jumps is mainly controlled by a random measure which is generated by a Lévy process with a Lévy measure f_θ(z)dz, and we admit the case ∫ f_θ(z)dz = ∞ in which infinitely many small jumps occur even in any finite time intervals. We propose an estimating function under this complicated situation and show the consistency and the asymptotic normality. Although the estimators in this paper are not completely efficient, the method can be applied to comparatively wide class of stochastic differential equations, and it is easy to compute the estimating equations. Therefore, it may be useful in applications. We also present some simulation results for some simple models. Final version 25 December 2004     

Infinite Horizon Reflected Backward SDEs with Jumps and RCLL Obstacle

Abstract

In this article, we deal with the one-dimensional reflected backward stochastic differential equation with one or two barriers for infinite horizon when the noise is driven by a Brownian motion and an independent Poisson point process. The reflecting process is right continuous with left limits whose jumps are whatever. The authors prove existence and uniqueness of the solution by using a method based on a combination of penalization and the Snell envelope theory. Once more we use a contraction to show the result in the general framework.     

带随机跳跃的线性二次非零和微分对策问题

对于一类以布朗运动和泊松过程为噪声源的正倒向随机微分方程,在单调性假设下,给出了解的存在性和唯一性的结果．然后将这些结果应用于带随机跳跃的线性二次非零和微分对策问题之中,由上述正倒向随机微分方程的解得到了开环Nash均衡点的显式形式．     

A Generalized Renewal Equation for Perturbed Compound Poisson Processes with Two-Sided Jumps

Abstract

In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2 Gerber , H.U. , and Landry , B. 1998 . On the discounted penalty at ruin in a jump-diffusion and the perpetual put option . Insurance: Mathematics and Economics 22 : 263 – 276 .[Crossref], [Web of Science ®] , [Google Scholar]] where only downward jumps are allowed.     

Solutions and Multiple Solutions for p（x）-Laplacian Equations with Nonlinear Boundary Condition

The authors study the p（x）-Laplacian equations with nonlinear boundary condition. By using the variational method, under appropriate assumptions on the perturbation terms f1 （x, u）, f2（x, u） and h1（x）, h2（x）, such that the associated functional satisfies the ＂mountain pass lemma＂ and ＂fountain theorem＂ respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.