In this paper we present a general result concerning the convergence to stochastic integrals with non-linear integrands. The key finding represents a generalization of Chan and Wei’s (1988) Theorem 2.4. and that of Ibragimov and Phillips’ (2004) Theorem 8.2. This result is necessary for analysing the asymptotic properties of mis-specification tests, when applied to a unit root process, for whic...

We prove that the existence of a solution to a fully nonlinear elliptic equation in a bounded domain Ω with an overdetermined boundary condition prescribing both Dirichlet and Neumann constant data forces the domain Ω to be a ball. This is a generalization of Serrin’s classical result from 1971.

This article is devoted to define and solve an evolution equation of the form dyt = ∆yt dt + dXt(yt), where ∆ stands for the Laplace operator on a space of the form L(R), and X is a finite dimensional noisy nonlinearity whose typical form is given by Xt(φ) = ∑N i=1 x i tfi(φ), where each x = (x , . . . , x) is a γ-Hölder function generating a rough path and each fi is a smooth enough function d...

p-trigonometric functions are generalizations of the trigonometric functions. They appear in context of nonlinear differential equations and also in analytical geometry of the p-circle in the plain. The most important ptrigonometric function is sinp(x). For p > 1, this function is defined as the unique solution of the initial-value problem (|u′(x)|p−2u′(x))′ = (p− 1)|u(x)|p−2u(x), u(0) = 0, u′(...

In this paper, a displacement-constrained volume-minimizing topology optimization model is present for two-dimensional continuum problems. The new model is a generalization of the displacement-constrained volume-minimizing model developed by Yi and Sui [1] in which the displacement is constrained in the loading point. In the original model the displacement constraint was formulated as an equali...

The method of triangular functions (TF) could be a generalization form of the functions of block-pulse (Bp)‎. ‎The solution of second kind integral equations by using the concept of TF would lead to a nonlinear equations system‎. ‎In this article‎, ‎the obtained nonlinear system has been solved as a dynamical system‎. ‎The solution of the obtained nonlinear system by the dynamical system throug...

Amongst possible choices for identifying complicated processes for prediction, simulation, and approximation applications, high-order Takagi-Sugeno (TS) fuzzy models are fitting tools. Although they can construct models with rather high complexity, they are not as interpretable as first-order TS fuzzy models. In this paper, we first propose to use Deformed Linear Models (DLMs) in consequence pa...

We suggest a generalization of the notion of invariance of a given partial differential equation with respect to Lie-Bäcklund vector field. Such generalization proves to be effective and enables us to construct principally new Ansätze reducing evolution-type equations to several ordinary differential equations. In the framework of the said generalization we obtain principally new reductions of ...