We provide necessary and sucient conditions for psi-conditional as-ymptotic stability of the solution of a linear matrix Lyapunov system and sucientconditions for psi -conditional asymptotic stability of the solution of a rst ordernon-linear matrix Lyapunov system X0 = A(t)X + XB(t) + F(t;X).

We first show asymptotic L bounds for a class of equations, which includes the Burger-Sivashinsly model for odd solutions with periodic boundary conditions. We consider the conditional stability of stationary solutions of Kuramoto-Sivashinsky equation in the periodic setting. We establish rigorously the general structure of the spectrum of the linearized operator. In addition, we show condition...

We consider the sensitivity of conditional value-at-risk (CVaR) with respect to the tail index assuming regularly varying tails and exponential and faster-than-exponential tail decay for the return distribution. We compare it to the CVaR sensitivity with respect to the scale parameter for stable Paretian, the Student’s t, and generalized Gaussian laws and discuss implications for the modeling o...

The design of artificial agents that are meant to model behavioral, cognitive, economic or social structures asks for tools that aid in layout and implementation of agent architectures. To implement agents based on Dörner’s Psi theory of emotion and cognition, our group has introduced a toolkit that assists in designing modular architectures, as well as representational structures, such as sema...

We find two-sided estimates for the best uniform approximations of classes convolutions 2????-periodic functions from a unit ball space Lp,1 ? p < ?; with fixed kernels such that moduli their Fourier coefficients satisfy condition $$ \sum \limits_{k=n+1}^{\infty}\psi (k)<\psi (n) : In case (k)=o(1)\psi ; obtained become asymptotic equalities.

We describe the asymptotic behavior of conditional least squares estimator offspring mean for subcritical strongly stationary Galton–Watson processes with regularly varying immigration tail index ? ? ( 1 , 2 ) . The limit law is ratio two dependent stable random variables indices ? and 3 respectively, it has a continuously differentiable density function. use point process technique in proofs.