Related papers: On the existence of some ARCH($\infty$) processes
The paper is devoted to the investigation of the solvability of an integro-differential equation in the case of the double scale anomalous diffusion with a sum of two negative Laplacians in different fractional powers in R^3. The proof of…
Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility for a general class of motility functions $\gamma$ which may in particular decay in an arbitrary way at infinity. Assuming further…
In this paper conditions, under which an integro-differential operator is a linear automorphism, are provided. Alternatively, the problem can be considered in terms of existence of a unique formal power series solution for a linear Cauchy…
In this paper we prove the existence of steady multiple vortex patch solutions to the vortex-wave system in a planar bounded domain. The construction is performed by solving a certain variational problem for the vorticity and studying its…
We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…
We explain how H\"ormander's classical solution of the dbar-equation in the plane with a weight which permits growth near infinity carries over to the rather opposite situation when we ask for decay near infinity. Here, however, a natural…
Our aim in this work is to give explicit formula of the linear processes solution of autoregressive time series AR(2) with hint of generating functions theory by using the Horadam numbers and polynomials.
We provide sufficient conditions on the coefficients of a stochastic functional differential equation with bounded memory driven by Brownian motion which guarantee existence and uniqueness of a maximal local and global strong solution for…
We prove the existence of stationary solutions for some systems of reaction-diffusion type equations with superdiffusion in the corresponding H^2 spaces. Our method is based on the fixed point theorem when the elliptic problems contain…
A sufficient condition of regularity for solutions to the Navier-Stokes equations is proved. It generalizes the so-called $L_{3,\infty}$-case.
This paper is concerned with the implications of sufficient conditions ensuring that a perturbation of a frame is again a frame. We emphasize how stability of frames is fundamental for numerical applications and we discuss in particular the…
Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first…
We establish a priori $L^\infty$-estimates for non-negative solutions of a semilinear nonlocal Neumann problem. As a consequence of these estimates, we get non-existence of non-constant solutions under suitable assumptions on the diffusion…
This paper deals with the existence of asymptotic almost automorphic solution of fractional integro differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz…
This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…
We give sufficient conditions for a discrete set of points in any dimensional real hyperbolic space to have positive anchored expansion. The first condition is a bounded mean density property, ensuring not too many points can accumulate in…
Causality and stability are fundamental requirements for the differential equations describing predictable relativistic many-body systems. In this work, we investigate the stability and causality criteria in linear mode analysis. We discuss…
Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at $\aleph_{\omega_1}$, answering a question of Ben-Neria, Hayut, and Unger: We…
We study the solutions of a generalized Allen-Cahn equation deduced from a Landau energy functional, endowed with a non-constant higher order stiffness. We assume the stiffness to be a positive function of the field and we discuss the…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…