The paper introduces a new autoregressive model of order one for time seriesof counts. is comprised linear as well bilinear component. These two components are governed by random coefficients. autoregression achieved using the negative binomial thinning operator. method moments and conditional maximum likelihood discussed parameter estimation. practicality presented on real data set.

This is a short review of the Kadomtsev–Petviashvili hierarchies types $$\mathrm{B}$$ and $$\mathrm{C}$$ . The main objects are $$L$$ operator, wave auxiliary linear problems for function, bilinear identity tau function. All them discussed in paper. Connections with usual (type- $$\mathrm{A}$$ ) hierarchy clarified. Examples soliton solutions dispersionless limit also considered.

Abstract We study the eigenvalue problem for a superlinear convolution operator in special case of bilinear constitutive laws and establish existence uniqueness one-parameter family nonlinear eigenfunctions under topological shape constraint. Our proof uses change scalar parameters applies Krein–Rutman arguments to linear substitute problem. also present numerical simulations discuss asymptotic...

We present a general result of approximate controllability for the bilinear Schrödinger equation (with wave function varying in the unit sphere of an infinite dimensional Hilbert space), under the hypothesis that the Schrödinger operator has discrete spectrum and that the control potential couples all eigenstates. The control method is based on a tracking procedure for the Galerkin approximatio...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method u...

We consider the composition of random i.i.d. aane maps of a Hilbert space to itself. We show convergence of the n'th composition in the Wasserstein metric via a contraction argument. The contraction condition involves the operator norm of the expectation of a bilinear form. This is contrasted with the usual contraction condition of a negative Lyapunov exponent. Our condition is stronger but eas...