Related papers: Strictly stationary solutions of spatial ARMA equa…
The present paper is a continuation of the author's previous works, in which necessary and sufficient local extrema at a stationary point of a polynomial or a power series (and thus of an analytic function) are given. It is known that for…
All stationary solutions to the one-dimensional nonlinear Schroedinger equation under box and periodic boundary conditions are presented in analytic form. We consider the case of repulsive nonlinearity; in a companion paper we treat the…
Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…
We establish the existence of non-stationary solutions to a symmetric system of second-order autonomous differential equations. Our technique is based on the equivariant degree theory and involves a novel characterization of orbit types of…
Approximate stationarity conditions provide necessary optimality conditions without requiring additional assumptions by demanding that a perturbed stationarity system possesses solutions as the involved perturbations tend to zero. Together…
We obtain exact moving and stationary, spatially periodic and localized solutions of a generalized discrete nonlinear Schr\"odinger equation. More specifically, we find two different moving periodic wave solutions and a localized moving…
This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which represents univariate nonstationary time series as stationary fluctuations around deterministic trend…
This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…
In this paper we discuss dynamic ARMA-type regression models for time series taking values in $(0,\infty)$. In the proposed model, the conditional mean is modeled by a dynamic structure containing autoregressive and moving average terms,…
A finite Larmor radius approximation is derived from the classical Vlasov equation, in the limit of large (and uniform) external magnetic field. We also provide an heuristic derivation of the electroneutrality equation in the finite Larmor…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
Dynamical systems governed by priority rules appear in the modeling of emergency organizations and road traffic. These systems can be modeled by piecewise linear time-delay dynamics, specifically using Petri nets with priority rules. A…
It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form…
In this paper we study solutions to multivariate stochastic delay differential equations (MSDDEs) which have stationary increments, and we show that this modeling framework is in many ways similar to the discrete-time cointegrated VAR…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
We construct a class of stationary, axisymmetric, horizonless spacetimes whose curvature is generated entirely by smooth, localised differential rotation $\Omega(r)$, while the spatial geometry remains exactly flat. Despite vanishing ADM…
The Nagumo lattice differential equation admits stationary solutions with arbitrary spatial period for sufficiently small diffusion rate. The continuation from the stationary solutions of the decoupled system (a system of isolated nodes) is…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…
In this paper, we consider the Whittle estimator for the parameters of a stationary solution of a continuous-time linear state space model sampled at low frequencies. In our context the driving process is a L\'evy process which allows…