Related papers: Stationary phase lemmas for general functions
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
Our proof is based on a generalization of action-angle variables, a convergent Lie transformation, and Moser's invariant curve theorem. As an overall outline we give a quick proof of Morris' original theorem. Then the full theorem is…
The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
A class of one-dimensional Fokker-Plank equations having a common stationary solution, which is a power function of the state of the process, was found. We prove that these equations also have generalized self-similar solutions which…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
Using stationary phase methods, we provide an explicit formula for the Melnikov function of the one and a half degrees of freedom system given by a Hamiltonian system subject to a rapidly oscillating perturbation. Remarkably, the Melnikov…
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…
Dynamical systems governed by priority rules appear in the modeling of emergency organizations and road traffic. These systems can be modeled by piecewise linear time-delay dynamics, specifically using Petri nets with priority rules. A…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…
We provide complete proofs of the lemmas about the properties of the regularized loss function that is used in the second order techniques for learning time-series with structural breaks in Osogami (2021). In addition, we show experimental…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
Superposition rules form a class of functions that describe general solutions of systems of first-order ordinary differential equations in terms of generic families of particular solutions and certain constants. In this work we extend this…
An important problem in time series analysis is the discrimination between non-stationarity and longrange dependence. Most of the literature considers the problem of testing specific parametric hypotheses of non-stationarity (such as a…
It was recently proved that any strictly stationary stochastic process can be viewed as an autoregressive process of order one with coloured noise. Furthermore, it was proved that, using this characterisation, one can define closed form…
We generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t),\alpha)$ so that the function $y$ and the order of fractional derivative $\alpha$ are varied in the minimization procedure. We derive…
In this paper we consider the problem on uniform estimates for generalized oscillatory integrals given by Mittag- Leffler functions with the homogeneous polynomial phase. We obtain a variant of Ricci-Stein Lemma and invariant estimates for…
We introduce some general and special formulations of general position theorem for parametrized families of fractals and explain the techniques of its application to prove the existence of self-similar sets with prescribed special…