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Iterated Random Functions and Slowly Varying Tails [PDF]
Stochastic Processes and their Applications, 2015 Consider a sequence of i.i.d. random Lipschitz functions $\{\Psi_n\}_{n \geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment assumptions this
Dyszewski, Piotr
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Further Results on Lyapunov Functions for Slowly Time-Varying Systems [PDF]
Mathematics of Control, Signals, and Systems, 2006 We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially ...
Malisoff, Michael, Mazenc, Frederic
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Distributed nash equilibrium seeking for heterogeneous second-order nonlinear noncooperative games with communication delays [PDF]
Scientific ReportsThis paper investigates the noncooperative game problems over weight-balanced digraphs with communication delays. Compared with existing noncooperative games, a class of noncooperative games that are more aligned with practical systems is discussed ...
Rui Yu +4 more
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On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications
MathematicsIn this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with
Azam A. Imomov +2 more
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The research of some classes of almost periodic at infinity functions [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 The article under consideration is devoted to continuous almost periodic at infinity functions defined on the whole real axis and with their values in a complex Banach space.
Vysotskaya, Irina A. +1 more
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Harmonic analysis of functions almost periodic at infinity in Banach modules [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2021 The article is devoted to homogeneous spaces of functions defined on a locally compact Abelian group and with their values in a complex Banach space.
Strukova, Irina Igorevna
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A Seneta's Conjecture and the Williamson Transform [PDF]
Sahand Communications in Mathematical Analysis, 2023 Considering slowly varying functions (SVF), %Seneta (2019) Seneta in 2019 conjectured the following implication, for $\alpha\geq1$,$$\int_0^x y^{\alpha-1}(1-F(y))dy\textrm{\ is SVF}\ \Rightarrow\ \int_{0}^x y^{\alpha}dF(y)\textrm{\ is SVF, as $x\to\infty$
Edward Omey, Meitner Cadena
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Boundary Value Problems, 2022 We consider the following singular semilinear problem { Δ u ( x ) + p ( x ) u γ = 0 , x ∈ D ( in the distributional sense ) , u > 0 , in D , lim | x | → 0 | x | n − 2 u ( x ) = 0 , lim | x | → ∞ u ( x ) = 0 , $$ \textstyle\begin{cases} \Delta u(x)+p(x)u^
Imed Bachar, Entesar Aljarallah
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Comptes Rendus. Mathématique, 2021 This paper proves the Baum–Katz theorem for sequences of pairwise independent identically distributed random variables with general norming constants under optimal moment conditions.
Thành, Lê Vǎn
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A generalization of slowly varying functions [PDF]
Proceedings of the American Mathematical Society, 1986 This note establishes that if the main part of the definition of a slowly varying function is relaxed to the requirement that lim sup x → ∞ ψ ( λ x ) / ψ ( x ...
Drasin, D., Seneta, E.
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