The waveguide invariant is typically defined using of normal modes or ray theory, but it can also be related to the wavenumber-integration method for calculating the acoustic field in a waveguide. In this letter, the Wiener-Khinchin Theorem is used to show that the autocorrelation of the wavenumber-integration kernel, when plotted versus wavenumber difference and frequency, contains striations ...

Abstract We study the tamed magnetohydrodynamics equations, introduced recently in a paper by author, perturbed multiplicative Wiener noise of transport type on whole space $${\mathbb {R}}^{3}$$ R 3 and torus {T}}^{3}$$ T . In fir...

An α-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter α > 0 represents a mean reversion force to zero. We generalize the notion of α-Wiener bridges to continuous functions α : [0, T ) → R. We show that if the limit limt↑T α(t) exists and is positive, then a general α-Wiener bridge is in fact a bridge in the sense that it converges to 0 at time T wi...

In this paper, we establish generalized sampling theorems, stability theorems and new inequalities in the setting of shift-invariant subspaces Lebesgue Wiener amalgam spaces with mixed-norms. A convergence theorem general iteration algorithms for some Lp→(Rd) are also given.

This paper presents analytical and Monte Carlo results for a stochastic gradient adaptive scheme that tracks a time-varying polynomial Wiener system [i.e., a linear time-invariant (LTI) filter with memory followed by a time-varying memoryless polynomial nonlinearity]. The adaptive scheme consists of two phases: 1) estimation of the LTI memory using the LMS algorithm and 2) tracking the time-var...

In this paper we introduce the concept of Wiener–Luxemburg amalgam spaces which are a modification more classical Wiener intended to address some shortcomings latter face in context rearrangement-invariant Banach function spaces. We and study their properties, including (but not limited to) normability, embeddings between them associate also amalgams quasi-Banach necessary generalisation then a...

We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai, Probab. Theory Relat. Fields 103, 1995, on the Wiener ...

In this paper we extend the results of 9] on the stochastic disturbance attenuation problem to a wider class of stochastic systems. We consider time-invariant stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic parameter perturbations. The aim is to develop an H 1 {type theory for such systems. The Ito equations considered ...

1. Stochastic Integration on Hilbert spaces 2 1.1. Gaussian measures on Hilbert spaces 2 1.2. Wiener processes on Hilbert spaces 6 1.3. Martingales on Banach spaces 7 1.4. Stochastic integration 8 1.5. Appendix: Stochastic integration w.r.t. cylindrical Wiener processes 12 2. Stochastic Di erential Equations on Hilbert spaces 13 2.1. Mild, weak and strong solutions 13 2.2. Existence and uniquen...

Complex networks abound in physical, biological and social sciences. Quantifying a network's topological structure facilitates network exploration and analysis, and network comparison, clustering and classification. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks, such as the R package QuACN. Wiener type indices are known to depe...