Convergence of Certain Functionals of Integral Fractional Processes

In this paper we consider the asymptotic behavior of functionals of processes of the form ∫ ₀ ^t u _s dB _s ^H , where B ^H is a fractional Brownian motion with Hurst parameter H, and u is a process with finite q-variation, q<1/(1−H). We establish the stable convergence of the corresponding fluctuations.     

R~n上扩散过程的代数式收敛

本文研究n维欧氏空间上的扩散过程在L2意义下的代数式收敛的情况,给出了判定代数式收敛的方法,并对两种特殊情形扩散算子进行了讨论.将所得判敛法应用于两个例子可得到精确的结果.     

Stochastic Taylor Expansions for Functionals of Diffusion Processes

In this article, a stochastic Taylor expansion of some functional applied to the solution process of an Itô or Stratonovich stochastic differential equation with a multi-dimensional driving Wiener process is given. Therefore, the multi-colored rooted tree analysis is applied in order to obtain a transparent representation of the expansion which is similar to the B-series expansion for solutions of ordinary differential equations in the deterministic setting. Further, some estimates for the mean-square and the mean truncation errors are given.     

关于次加泛函的一点注记

In this note we obtained a both sufficient and necessary condition there exist non-zero β′ degree abslutely homogeneous, continuous and subadditive unctionals in metric linear spaces (E, ‖·‖_β) for C < β≤β′ ≤1 . APPlying our result, a simpler proof of theorem in[1,§1] was given.     

Stochastic Taylor Expansions for the Expectation of Functionals of Diffusion Processes

Abstract

Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas w.r.t. increments of the time are presented for both, Itô and Stratonovich stochastic differential equation systems with multi-dimensional Wiener processes. Due to the very complex formulas arising for higher order expansions, an advantageous graphical representation by coloured trees is developed. The convergence of truncated formulas is analyzed and estimates for the truncation error are calculated. Finally, the stochastic Taylor formulas based on coloured trees turn out to be a generalization of the deterministic Taylor formulas using plain trees as recommended by Butcher for the solutions of ordinary differential equations.     

A Limit Theorem for Integral Functionals of an Extremum of Independent Random Processes

We prove a theorem on the convergence of integral functionals of an extremum of independent stochastic processes to a degenerate law of distributions.__________Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 2, pp. 214–221, February, 2005.     

A Contribution to the Theory of Quasilinear Elliptic Equations and Application to the Minimization of Integral Functionals

The aim of this work is to study the existence of solutions of quasilinear elliptic problems of the type

关于积分符号的注记

积分学是微积分的重要组成部分，而不定积分是整个积分学的基础，是运算的核心部分．本文主要通过历史和逻辑的角度对不定积分符号进行分析，并给出注记．     

关于积分符号的注记

积分学是微积分的重要组成部分,而不定积分是整个积分学的基础,是运算的核心部分.本文主要通过历史和逻辑的角度对不定积分符号进行分析,并给出注记.     

扩散过程代数式收敛定性的判别准则

本文定性地讨论非紧空间中可逆扩散过程的代数式收敛的判定 .使用分裂空间的方法 .将全空间分裂成两个部分 :紧的子空间与非紧的余子空间 .在紧子空间中考虑边界反射的Neumann过程 ,它必然是代数式收敛的 .而在非紧子空间中考虑边界吸收的Dirichlet过程 ,如果这一Dirichlet过程以代数式的速度击中边界 ,那么就有原过程在全空间代数式收敛 ;反之 ,原过程代数式收敛 ,非紧子空间中的Dirichlet过程也是代数式收敛的 .因此过程在紧子空间的任意摄动不会影响在全空间的代数式收敛性 .     

Convergence of Time Changed Skew Product Diffusion Processes

A limit theorem for the time changed skew product diffusion processes is investigated. Skew product diffusion processes are given by one dimensional diffusion processes and the spherical Brownian motion, and the time change is based on a positive continuous additive functional. It is shown that the limit process is corresponding to Dirichlet form of non-local type according to degeneracy of the limit measure of underlying ones. Some examples of limit processes are given which lead us to Dirichlet forms with diffusion term, jump term and killing term.     

Two-Scale Convergence of Integral Functionals with Convex, Periodic and Nonstandard Growth Integrands

We study the periodic homogenization for a family of functionals defined on Orlicz-Sobolev spaces. One fundamental in this topic is to extend the classical compactness results of the two-scale convergence method to this type of spaces.     

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Algebraic convergence in-sense is studied for the reflecting
diffusion processes on noncompact manifold with non-convex boundary. A series of sufficient
and necessary conditions for the algebraic convergence are presented.     

Stochastic Integral Representations of the Extrema of Time-homogeneous Diffusion Processes

The stochastic integral representations (martingale representations) of square integrable processes are well-studied problems in applied probability with broad applications in finance. Yet finding explicit expression is not easy and typically done through the Clack-Ocone formula with the advanced machinery of Malliavin calculus. To find an alternative, Shiryaev and Yor (Teor Veroyatnost i Primenen 48(2):375–385, 2003) introduced a relatively simple method using Itô’s formula to develop representations for extrema of Brownian motion. In this paper, we extend their work to provide representations of functionals of time-homogeneous diffusion processes based on the Itô’s formula.     

A Note on Strong Solutions to the Stokes System

We give an alternative and quite simple proof of existence of W ^2,q -W ^1,q -strong solutions for the Stokes system, endowed with Dirichlet boundary conditions in a bounded smooth domain.     

扩散过程代数式收敛比较判敛法

研究不同的马氏半群无穷小算子之间代数式收敛的关系,获得了若干比较定理.从而可将许多一般形式的扩散算子与特殊情形进行比较,将其化归为特殊的简单易算的情形.