Evaluation formulas for conditional abstract wiener integrals

In this paper we consider abstract Wiener space version of conditional Wiener integrals and establish formulas for evaluating conditional abstract Wiener integrals for various classes of functions on an abstract Wiener space. We then apply our formulas to evaluate certain Wiener integrals and conditional Wiener and Yeh-Wiener integrals     

Wiener indices of balanced binary trees

We study a new family of trees for computation of the Wiener indices. We introduce general tree transformations and derive formulas for computing the Wiener indices when a tree is modified. We present several algorithms to explore the Wiener indices of our family of trees. The experiments support new conjectures about the Wiener indices.     

Rough paths analysis of general Banach space-valued Wiener processes

In this article, we carry out a rough paths analysis for Banach space-valued Wiener processes. We show that most of the features of the classical Wiener process pertain to its rough path analog. To be more precise, the enhanced process has the same scaling properties and it satisfies a Fernique type theorem, a support theorem and a large deviation principle in the same Hölder topologies as the classical Wiener process does. Moreover, the canonical rough paths of finite dimensional approximating Wiener processes converge to the enhanced Wiener process. Finally, a new criterion for the existence of the enhanced Wiener process is provided which is based on compact embeddings. This criterion is particularly handy when analyzing Kunita flows by means of rough paths analysis which is the topic of a forthcoming article.     

Various topologies in the Wiener space and Lévy's stochastic area

Summary In this paper, we observe how Lévy's stochastic area looks when we see it through various topologies in the Wiener space. Our theorem implies that it is quite natural from the viewpoint of topology to define a distinct skeleton of Lévy's stochastic areaS(w) for each distinct topology in the Wiener space, or equivalently, for each distinct abstract Wiener space on which the Wiener measure andS(w) are realized. Thus we cannot determine its intrinsic skeleton in the theory of abstract Wiener spaces.     

Wiener Algebra for the Quaternions

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener–Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener–Hopf operators.     

大偏差与l~p-值Wiener过程在Hlder范数下的泛函连续模

本文在Holder范数生成的强拓扑下,建立了l~2-值Wiener过程的大偏差公式,从而得到了l~2-值与l~p-值Wiener过程在Holder范数下的泛函连续模.     

On the Convergence of the P-Algorithm for One-Dimensional Global Optimization of Smooth Functions

The Wiener process is a widely used statistical model for stochastic global optimization. One of the first optimization algorithms based on a statistical model, the so-called P-algorithm, was based on the Wiener process. Despite many advantages, this process does not give a realistic model for many optimization problems, particularly from the point of view of local behavior. In the present paper, a version of the P-algorithm is constructed based on a stochastic process with smooth sampling functions. It is shown that, in such a case, the algorithm has a better convergence rate than in the case of the Wiener process. A similar convergence rate is proved for a combination of the Wiener model-based P-algorithm with quadratic fit-based local search.     

A Wiener Chaos Approach to Hyperbolic SPDEs

We construct generalized weighted Wiener chaos solutions for hyperbolic linear SPDEs driven by a cylindrical Brownian motion. Explicit conditions for the existence, uniqueness, and regularity of generalized (Wiener Chaos) solutions are established in Sobolev spaces. An equivalence relation between the Wiener Chaos solution and the traditional one is established. The Heath–Jarrow–Morton (HJM) forward rate model is used as an example to illustrate the general construction.     

LINEAR ISOMETRIC NON-ANTICIPATIVE TRANSFORMATIONS OF WIENER PROCESS

ThispaperisanoutcomeofnumerousdiscusionsandexchangeofideaswithlatePredragPerunicic,whosedeepandprofoundmathematicalknowledgeandhumanvaluesgaveusaninspirationandmotivationtofinalizeourjointideas.1.Wereferto[3,4]forthenotionofspectralmultiplicitytheoryintheseparableHilbertspace.LetHbeacyclicHilbertspacewiththeresolutionoftheidentity{p(t)}ofthemaximalspectraltypelIP(dt)ll'~dt-ordinaryLebesguemeasure.Anon-anticipativelineartransformationsisdefinedbyVolterrakernelg(t,u),uSt,ajsf'g(t)u)p(du),t>0…     

The local times and Hausdorff measure for level sets of a Wiener sheet

In this paper, we discuss the relation between the local times and the level sets of a Wiener sheet, and give moment estimates for the local times of a Wiener sheet. We show that the correct Hausdorff measure function for level sets of N-parameter Rd-valued Wiener sheet is (r)=rN-d/2(loglog1/r)d/2 if 2N＞d. This solves the problem posed by S. J. Taylor.     

Evaluation Formulas for a Conditional Feynman Integral Over Wiener Paths in Abstract Wiener Space

In this paper, we introduce a simple formula for conditional Wiener integrals over , the space of abstract Wiener space valued continuous functions. Using this formula, we establish various formulas for a conditional Wiener integral and a conditional Feynman integral of functionals on in certain classes which correspond to the classes of functionals on the classical Wiener space introduced by Cameron and Storvick. We also evaluate the conditional Wiener integral and conditional Feynman integral for functionals of the form which are of interest in Feynman integration theories and quantum mechanics.     

The composition of Wiener functionals with non absolutely continuous Shifts

Summary In this paper we study some classes of Wiener functionals whose elements can be composed with a non-linear, non-absolutely continous transformation of the form of perturbation of identity in the direction of Cameron-Martin space. We show that under certain conditions the image of the Wiener measure under the above transformation induces a generalized Wiener functional on certain Sobolev spaces generalizing the Radon-Nikodym relation to non absolutely continuous transformations. A series representation for the generalized Radon-Nikodym derivative is presented and conditional expectations of some generalized random variables are considered.     

Dynamics of stochastic partly dissipative systems on time-varying domain

This article is devoted to stochastic partly dissipative systems (SPDS) defined on time-varying domain expending in time. The definition of a space–time trace class Wiener process on time-varying domain is presented by combining a time trace class Wiener process with a spatial intensity defined on time-varying domain. Some nice properties for Wiener process on time-varying domain are also presented. We develop a new penalty method to establish the existence and uniqueness of variational solution of SPDS with additive noise on time-varying domain. The existence of global attractor for the process generated by variational solution is also obtained.     

The wavelet transform for Wiener functionals and some applications

The wavelet transform is defined for Wiener functionals. We characterize global and local regularities of Wiener functionals and we give a criterion for the existence and regularity of densities. Such a criterion is applied to diffusion processes and to the solutions to backward stochastic differential equations.     

Hausdorff measures on the Wiener space

We construct a Hausdorff measure of finite co-dimension on the Wiener space. We then extend the Federer co-area Formula to this Wiener space for functions with the sole condition that they belong to the first Sobolev space. An explicit formula for the density of the images of the Wiener measure under such functions follows naturally from this. As a corollary, this yields a new and easy proof of the Krée-Watanabe theorem concerning the regularity of the images of the Wiener measure.     

关于分数Wiener过程的不可微连续

在本文中，我们推广了Csoego＂和Shao(1994)的结果，给出了阶α（0＜α＜1）的分数Wiener过程的不可微连续模。     

Stochastic integration,trace and the skeleton of wiener functionals

It is shown that the notion of trace induced by a given complete orthonormal system relates the Skorohod integral with a corresponding Ogawa‐type integral evaluated with respect to the same orthonormal systems. Similarly the multiple Wiener‐Ito integral is shown to be related to a multiple Ogawa‐type integral induced by a complete orthonormal system via the Hu‐Meyer formula with suitably defined multiple traces. The notion of skeleton of a Wiener functional relative to a given orthonormal system is defined and yields what seems to be a “natural” extension of Wiener functionals to the Cameron Martin space and the Wiener processes with a different scale.     

Enumeration of Wiener indices in random polygonal chains

The Wiener index of a connected graph (molecule graph) G is the sum of the distances between all pairs of vertices of G, which was reported by Wiener in 1947 and is the oldest topological index related to molecular branching. In this paper, simple formulae of the expected value of the Wiener index in a random polygonal chain and the asymptotic behavior of this expectation are established by solving a difference equation. Based on the results above, we obtain the average value of the Wiener index of all polygonal chains with n polygons. As applications, we use the unified formulae to obtain the expected values of the Wiener indices of some special random polygonal chains which were deeply discussed in the context of organic chemistry or statistical physics.     

Note on calculating wiener numbers of molecular graphs with symmetry

The authors provided a simple method for calculating Wiener numbers of moleculargraphs with symmetry in 1997. This paper intends to further improve on it and simplifies thecalculation of the Wiener numbers of the molecular graphs.     

A Crowning Moment for Wiener Indices

The Wiener (Sum of All Distances) Index for three out of the four classes of hexagonal models or regular planar hex-patterns used to model graphite and similar structures have been known for a few years. In this paper we find the Wiener Index for the Crown or Beehive hexagonal model.