具有非倍测度的参数型Marcinkiewicz积分交换子在Hardy空间的有界性

主要证明了由参数型Marcinkiewicz积分M~p和Lipschitz函数b生成的交换子M_b~p的有界性.在M的核满足一定的条件下,证明了M_b~p不仅从Lebesgue空间L~(n/(n-β))(μ)到Hardy空间H~1(μ)有界,而且从Lebesgue空间L~(n/β)(μ)到RBMO(μ)有界.     

Generalized area operators on L^p（R^n）

We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces R＋^n＋1. The characterization of the boundedness and compactness of the generalized area operator from LP（]Rn） to Lq（IRn） is investigated in terms of s-Carleson measures with 1 〈 p, q 〈 ＋∞. In the case of p = q = 1, the weak type estimate is also obtained.     

On intensities of perturbed random measures on Hausdorff spaces

Abstract

This article studies classes of random measures on topological spaces perturbed by stochastic processes (a.k.a. modulated random measures). We render a rigorous construction of the stochastic integral of functions of two variables and showed that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. Mathematical formalism of integral-driven random measures and their stochastic intensities find numerous applications in stochastic models, physics, astrophysics, and finance that we discuss throughout the article.     

Occupation measure functionals in merging phase space

This paper deals with the averaging and diffusion approximation for occupation time of general phase space semi-Markov processes under split with simple and double merging in a series scheme. These results seem to be particularly interesting since the variance coefficient is obtained in a simple form. The method of proof of weak convergence results here is based on the construction of the compensating operator of the extended Markov renewal processes and on the solution of the singular perturbation problem of this operator acting on test functions.     

Itô-Wiener Chaos Expansion with Exact Residual and Correlation, Variance Inequalities

We give a formula of expanding the solution of a stochastic differential equation (abbreviated as SDE) into a finite Itô-Wiener chaos with explicit residual. And then we apply this formula to obtain several inequalities for diffusions such as FKG type inequality, variance inequality and a correlation inequality for Gaussian measure. A simple proof for Houdré-Kagan's variance inequality for Gaussian measure is also given.     

Vector measure as controls for explicit nonlinear impulsive system of fed-batch culture

In this paper, we consider an optimal control problem of microbial fermentation process in which glycerol is converted to 1,3-propanediol by Klebsiella pneumoniae in fed-batch culture. During the period of reaction, the variation of pH value is monitored to determine glycerol replenishment quantity, guaranteeing that microorganism can always keep growing fast under enough nutrition. Every time pH value is lower than seven, the quantity of glycerol added is such that pH value returns seven again. Glycerol is poured into reactor at discrete time instant and the quantity is controllable. The problem is to determine for each discrete time instant the glycerol quantity to add and maximize the final concentration of 1,3-propanediol. We present a controlled explicit nonlinear impulsive dynamical system of fed-batch culture with state independent vector measures as controls and study the existence, uniqueness, boundedness, continuous dependence and Gâteaux differentiability of its solution with respect to controls. We then propose a multiple objective programming model and demonstrate the regularity of cost functionals and weak compactness of admissible control set. Finally we discuss the existence of optimal control and implement a hybrid particle swarm optimization algorithm to solve the model optimally. Computational results are presented on a numerical example.     

Convergence of numerical solutions for variable delay differential equations driven by Poisson random jump measure

We study the following stochastic differential delay equations driven by Poisson random jump measure