Martingale problems for switched processes

Sufficient and necessary conditions are given for existence and uniqueness for the martingale problem associated with weakly coupled operator. Some result of convergence of martingale solutions is also obtained.     

齐次超曲面上测度Fourier变换的平均衰减估计

该文主要考虑限制在齐次超曲面上的测度dμ的Fourier变换的L^q范数估计. 基于此结论, 还得到了一些有关卷积算子Tf(x, θ)=f *μ_θ(x)的混合范数不等式.     

A new characterization of <Emphasis Type="Italic">p</Emphasis>-smoothable Banach spaces

In this paper an atomic decomposition theorem for Banach-space-valued weak Hardy regular martingale space w _p H _α ^S (X) is given. As an application, p-smoothable Banach spaces are characterized in terms of bounded sublinear operators defined on Banach-space-valued weak Hardy regular martingale space w _p H _α ^S (X).     

Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier–Stokes equations driven by Lévy processes

In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier–Stokes equations driven by Lévy processes consisting of the Brownian motion, the compensated Poisson random measure and the Poisson random measure are considered in a bounded domain. We obtain the existence of martingale solutions. The construction of the solution is based on the classical Galerkin approximation method, the stopping times, the stochastic compactness method and the Jakubowski–Skorokhod theorem.     

Martingale solutions of nematic liquid crystals driven by pure jump noise in the Marcus canonical form

In this work we consider a stochastic evolution equation which describes the system governing the nematic liquid crystals driven by a pure jump noise in the Marcus canonical form. The existence of a martingale solution is proved for both 2D and 3D cases. The construction of the solution relies on a modified Faedo–Galerkin method based on the Littlewood–Paley-decomposition, compactness method and the Jakubowski version of the Skorokhod representation theorem for non-metric spaces. We prove that in the 2-D case the martingale solution is pathwise unique and hence deduce the existence of a strong solution.     

About the rate function in concentration inequalities for suprema of bounded empirical processes

We provide new deviation inequalities in the large deviations bandwidth for suprema of empirical processes indexed by classes of uniformly bounded functions associated with independent and identically distributed random variables. The improvements we get concern the rate function which is, as expected, the Legendre transform of the suprema of the log-Laplace transform of the pushforward measure by the functions of the considered class (up to an additional corrective term). Our approach is based on a decomposition in martingale together with some comparison inequalities.     

Martingale solutions of a stochastic wave equation with reflection

We discuss an initial boundary value problem for a one-dimensional stochastic wave equation with reflection. For stochastic parabolic equations with reflection, there are some well-known results. However, there seems to be no existence result for a stochastic wave equation with reflection. Even for a deterministic wave equation, the problem has not been completely resolved. Our goal is to establish the existence of a martingale solution for this problem.     

随机微分方程弱解的稳定性和存在性

本文研究了驱动项为无穷维Ｂｒｏｗｎ运动的一般Ｉｔ随机微分方程，给出了还问题的解和弱解的存在性关系，证明了在线性增长条件下，方程弱解的稳定性和存在性定理．     

Optimal portfolio strategies benchmarking the stock market

The paper investigates the impact of adding a shortfall risk constraint to the problem of a portfolio manager who wishes to maximize his utility from the portfolios terminal wealth. Since portfolio managers are often evaluated relative to benchmarks which depend on the stock market we capture risk management considerations by allowing a prespecified risk of falling short such a benchmark. This risk is measured by the expected loss in utility. Using the Black–Scholes model of a complete financial market and applying martingale methods, explicit analytic expressions for the optimal terminal wealth and the optimal portfolio strategies are given. Numerical examples illustrate the analytic results.