We propose residual based tests for cointegration using local GLS detrending (Elliott, Rothemberg and Stock, 1996, ERS) applied separately to each variable of the system. We consider two cases, one where only a constant is included and one where a constant and a time trend are included. We derive the asymptotic distribution of a feasible point optimal test which allows us to derive the power en...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...

We are interested in the long time behavior of a two-type density-dependent biological population conditioned on non-extinction, in both cases of competition or weak cooperation between the two species. This population is described by a stochastic Lotka-Volterra system, obtained as limit of renormalized interacting birth and death processes. The weak cooperation assumption allows the system not...

Using the general notion of distance function introduced in [2], a construction of the finest distance structure (d, M, P ) that induces a given quasiuniformity is given, which leads to a concrete, full, and co-reflective embedding of the category of quasi-uniformities into that of distance spaces. Moreover, when the usual defining condition xUεy :⇔ d(y, x) 6 ε of the basic entourages is genera...

We study the generalized Ulam-Hyers stability, the well-posedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the so-called α-β-contraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.