Asymptotics are obtained for the mean, variance and higher moments as well as for the distribution of the Wiener index of a random tree from a simply generated family (or, equivalently, a critical Galton– Watson tree). We also establish a joint asymptotic distribution of the Wiener index and the internal path length, as well as asymptotics for the covariance and other mixed moments. The limit l...

We characterize the asymptotic independence between blocks consisting of multiple Wiener-Itô integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its multidimensional extension, and other related results on the multivariate convergence of multiple Wiener-Itô integrals, that involve Gaussian and non Gaussian limits. We give ...

We show that for certain bounded cylinder functions of the form F(x) = μ̂((h1,x)∼, . . . ,(hn,x)∼), x ∈ B, where μ̂ :Rn → C is the Fourier-transform of the complexvalued Borel measure μ on (Rn), the Borel σ -algebra of Rn with ‖μ‖ < ∞, the analytic Feynman integral of F exists, although the analytic Feynman integral, limz→−iq Iaw(F ;z)= limz→−iq(z/2π) ∫ Rn f( →u)exp{−(z/2)| →u|2}d →u, do not alwa...

In his fundamental research on generalized harmonic analysis, Wiener proved that the integrated Fourier transform defined by Wf(γ) = ∫ f(t) (e−2πiγt − χ[−1,1](t))/(−2πit) dt is an isometry from a nonlinear space of functions of bounded average quadratic power into a nonlinear space of functions of bounded quadratic variation. We consider this Wiener transform on the larger, linear, Besicovitch ...

Whereas there is an exact linear relation between the Wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal Wiener indices exhibit a completely different behavior: Correlation between terminal Wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. In this article, we analyze the basic properties of terminal Wiener indices...

Problems of Nehari type are studied for matrix valued k-variable almost periodic Wiener functions: Find contractive k-variable almost periodic Wiener functions having prespeciied Fourier coeecients with indices in a given halfspace of R k. We characterize the existence of a solution, give a construction of the solution set, and exhibit a particular solution that has a certain maximizing propert...

Let ω be a regular measure on the unit circle and let p > 0. We establish asymptotic behavior, as n→∞, for the Lp Christoffel function λn,p (ω, z) = inf deg(P )≤n−1 ∫ π −π ∣∣P (eiθ)∣∣p dω (θ) |P (z)| at Lebesgue points z on the unit circle, where ω′ is lower semi-continuous. While bounds for these are classical, asymptotics have never been established for p 6= 2. The limit involves an extremal ...

Many nonlinear systems can be described by a Wiener-Schetzen model. In this model, the linear dynamics are formulated in terms of orthonormal basis functions (OBFs). The nonlinearity is modeled by a multivariate polynomial. In general, an infinite number of OBFs is needed for an exact representation of the system. This paper considers the approximation of a Wiener system with finite-order infin...

Wiener process with instantaneous reflection in narrow tubes of width ε ≪ 1 around axis x is considered in this paper. The tube is assumed to be (asymptotically) non-smooth in the following sense. Let V (x) be the volume of the cross-section of the tube. We assume that 1 ε V (x) converges in an appropriate sense to a non-smooth function as ε ↓ 0. This limiting function can be composed by smooth...

The construction, in [1], of a pseudodifferential calculus analogous to the Weyl calculus, an infinite dimensional setting, required introduction convenient symbol classes. symbols are functions defined on Hilbert space H, which compels us investigate, particular, their stochastic extensions Wiener linked with H.