关于白噪声的L2—泛函在Malliavin算子作用下的积分表示

本文基于非线性空间的张量积结构，建立了抽象可测空间上关于白噪声测度Ｘ的随机积分。     

白噪声分析中广义算子值函数的Bochner-Wick积分

白噪声广义算子在白噪声分析理论及其应用中起着十分重要的作用. 本文主要讨论了白噪声广义算子值函数的积分及相关问题. 主要工作有: 引入了广义算子值测度的概念, 分别讨论了这种测度在象征和算子p-范数意义下的变差及相互关系; 借助于广义算子的Wick积运算, 引入了广义算子值函数关于广义算子值测度的一种积分---Bochner-Wick积分, 讨论了这种积分的性质, 建立了相应的收敛定理并且展示了其在量子白噪声理论中的应用; 探讨了Bochner-Wick积分的Fubini定理及相关问题.     

φ^＊—值鞅测度的表示定理

本文研究了Ｌ（Φ~＊,Ψ~＊）值随机过程关于Φ~＊－值鞅测度的随机积分和Φ~＊值鞅测度的表示定理．     

关于n维参数强鞅的随机积分

在本文中定义了PK_(r)可料过程(见定义2.3)Φ(ξ~1,…,ξ~r),(ξ~q∈R_+~n,1≤g≤r≤n)关于n维参数强鞅组M=(M_1,…,M_r,)的r重随机积分。利用这些随机积分能表示满足适当条件的强鞅泛函,特别,n维参数Wienor过程的平方可积泛函和鞅能用这些积分来表示。     

BD全空间一个积分泛函的下半连续结果

本文研究定义在有界变差函数空间BD(Ω)上如下形式的积分泛函,得到了这个积分泛函关于L~1强收敛的下半连续性结果．,这里||A||*:= ■|(Aξ,ξ)|是对称矩阵A∈M_(sym)~(N×N)的最大特征值．     

关于中值公式两边取极限的理解

关于中值公式两边取极限的理解陈大均（华南建设学院西院）在证明连续函数ｆ（Ｘ）取变上限Ｘ的定积分的导数Φ（Ｘ）＝ｆ（ｘ）时，常应用积分中值公式取极限△ｘ→０，由于ｆ（Ｘ）连续，关于这一极限可作如下理解，注意到ξ＝Ｘ＋θ△Ｘ，（０＜θ＜１），可看成函数符...     

L~2空间中的均方随机积分

本文在Ｌ￣２（ｄｕ）空间中定义了比Ｒｉｃｍａｎｎ均方积分更为广泛的一种均方随机积分，并讨论了这种积分的性质及随机积分可交换顺序定理。     

关于图的最大亏格的一个定理改进

一个图G的最大亏格γM（G）主要由其参数Betti亏数ξ（G）确定．本文改进Nebesky文［5］中关于ξ（G）的一个表示定理，从而得到关于ξ（G）的一个新结果；由此，给出几个已有结果的简单证明，且其中推广文［8］中的一个结果．     

L2空间中的均方随机积分

本文在Ｌ²（ｄｕ）空间中定义了比Ｒｉｃｍａｎｎ均方积分更为广泛的一种均方随机积分，并讨论了这种积分的性质及随机积分可交换顺序定理。     

白噪声分析中的梯度算子和散度算子

在白噪声分析的框架中，我们给出了广义Weiner泛函空间上的梯度算子和散度算子的定义与公式，并利用梯度和散度算子以及适应投影建立了广义泛函的表示公式．也证明了积分核算子可用梯度与散度算子表出．     

Integral Kernel Operators on Fock Space – Generalizations and Applications to Quantum Dynamics

A general theory of operators on Boson Fock space is discussed in terms of the white noise distribution theory on Gaussian space (white noise calculus). An integral kernel operator is generalized from two aspects: (i) The use of an operator-valued distribution as an integral kernel leads us to the Fubini type theorem which allows an iterated integration in an integral kernel operator. As an application a white noise approach to quantum stochastic integrals is discussed and a quantum Hitsuda–Skorokhod integral is introduced. (ii) The use of pointwise derivatives of annihilation and creation operators assures the partial integration in an integral kernel operator. In particular, the particle flux density becomes a distribution with values in continuous operators on white noise functions and yields a representation of a Lie algebra of vector fields by means of such operators.     

Stochastic evolution equations in locally convex space

Ito’s stochastic integral is defined with respect to a Wiener process taking values in a locally convex space and Ito’s formula is proved. Existence and uniqueness theorem is proved in a locally convex space for a class of stochastic evolution equations with white noise as a stochastic forcing term. The stochastic forcing term is modelled by a locally convex space valued stochastic integral.     

Noncommutative itô and stratonovich noise and stochastic evolutionsand stratonovich noise and stochastic evolutions

We complete the theory of noncommutative stochastic calculus by introducing the Stratonovich representation. The key idea is to develop a theory of white noise analysis for both the Itô and Stratonovich representations based on distributions over piecewise continuous functions mapping into a Hilbert space. As an example, we derive the most general class of unitary stochastic evolutions, where the Hilbert space is the space of complex numbers, by first constructing the evolution in the Stratonovich representation where unitarity is self-evident.     

Some recent results in finitely additive white noise theory

We present a short survey of some very recent results on the finitely additive white noise theory. We discuss the Markov property of the solution of a stochastic differential equation driven directly by a white noise, study the Radon-Nikodym derivative of the measure induced by nonlinear transformation on a Hilbert space with respect to the canonical Gauss measure thereon and obtain a representation for nonlinear filter maps.     

Strong convergence for explicit space–time discrete numerical approximation methods for stochastic Burgers equations

In this paper we propose and analyze explicit space–time discrete numerical approximations for additive space–time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the stochastic Burgers equation with space–time white noise. The main result of this paper proves that the proposed explicit space–time discrete approximation method converges strongly to the solution process of the stochastic Burgers equation with space–time white noise. To the best of our knowledge, the main result of this work is the first result in the literature which establishes strong convergence for a space–time discrete approximation method in the case of the stochastic Burgers equations with space–time white noise.     

Quantum Laplacian and Applications

In this paper, we give an explicit solution of some linear quantum white noise differential equations by applying the convolution calculus on a suitable distribution space. In particular, we give an integral representation for the solution of the quantum heat equation.     

Fractional stochastic integration and Black–Scholes equation for fractional Brownian model with stochastic volatility

We modify the Hu-Øksendal and Elliot-van der Hoek approach to arbitrage-free financial markets driven by a fractional Brownian motion that is defined on a white noise space. We deduce and solve a Black–Scholes fractional equation for constant volatility and outline the corresponding equation with stochastic volatility. As an auxiliary result, we produce some simple conditions implying the existence of the Wick integral w.r.t. fractional noise.     

布朗随机流动形:白噪声分析方法

本文在经典白噪声分析框架下,用一种新的方法研究随机流动形. 首先使用布朗运动的Wick积分定义Wick型随机流动形.进一步, 用白噪声分析方法和S-变换证明：布朗随机流动形可视为Hida广义泛函.     

A new class of generalized nonlinear functionals of white noise with application to random integral equations ∗

In this paper we introduce some new classes of generalized nonlinear functionals of White noise which have integral representation with kernels either belonging to any L_p (1 ≤ p ≤ ∞)space or any Sobolev space W ^{P, s} for any real s and(1 ≤ p ≤ ∞)Our results extend the class of generelized nonlinear functionals of white noise originally developed by Hida [6, 7, 8] and greatly broaden their scope for application. We conclude the paper with an example involving random integral equations arising from Heat equation excited by White noise on the boundary.     

Complex White Noise and Coherent State Representations

An infinite-dimensional extension of a coherent state representation is discussed within the framework of white noise calculus. The exponential vectors (unnormalized coherent states) and the complex Gaussian integral play a role in such representations of a white noise function and of a white noise operator.