Related papers: Stationary phase lemmas for general functions
We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
We propose an explicit construction of a stationary solution for a stochastic recursion of the form $X\circ\theta=\phi(X)$ on a partially-ordered Polish space, when the monotonicity of $\phi$ is not assumed. Under certain conditions, we…
In this paper we present a multidimensional version of the van der Corput lemma where the decay of the oscillatory integral is gained with respect to all space variables, connecting the standard one-dimensional van der Corput lemma with the…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
In this paper using Sperner's lemma for modified partition of a simplex we will constructively prove Brouwer's fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions.
In this note, we provide a simple derivation of expressions for the restricted partition function and its polynomial part. Our proof relies on elementary algebra on rational functions and a lemma that expresses the polynomial part as an…
The proof of Brouwer's fixed-point theorem based on Sperner's lemma is often presented as an elementary combinatorial alternative to advanced proofs based on algebraic topology. The goal of this note is to show that: (i) the combinatorial…
We consider the phase-integral method applied to an arbitrary ordinary linear differential equation of the second-order and study how its symmetries affect the connection matrices associated with its general solution. We reduce the obtained…
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two…
We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
We construct solution operators to the $\overline{\partial}$-equation that depend continuously on the domain. This is applied to derive a parameter version of Forstneri\v{c}'s splitting lemma: If both the maps and the domains they are…
Multivariate process satisfying affine stochastic recurrence equation with generic diagonal matrices is considered. We prove that the stationary solution is regularly varying. The results are applicable to diagonal autoregressive models.
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
In this paper we consider a class of differential equations with state-dependent delays. We show first and second-order differentiability of the solution with respect to parameters in a pointwise sense and also using the C-norm on the…