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We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point will be a calibrated subaction for the doubling map on the…
We examine the sum of modified Bessel functions with argument depending non-linearly on the summation index given by \[S_{\nu,p}(a)=\sum_{n\geq 1} (an^p/2)^{-\nu} K_\nu(an^p)\qquad (a>0,\ 0\leq\nu<1)\] as the parameter $a\to 0+$, where $p$…
In stepwise derivations of programs from specifications, data type refinements are common. Many data type refinements involve isomorphic mappings between the more abstract and more concrete data representations. Examples include refinement…
Much of the progress in the gravitational self-force problem has involved the use of singular perturbation techniques. Yet the formalism underlying these techniques is not widely known. I remedy this situation by explicating the foundations…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
This paper addresses the challenges of embedding common droop control characteristics in ac-dc power system steady-state simulation and optimization problems. We propose a smooth approximation methodology to construct differentiable…
In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation…
Superconformal transformations are derived for the $\N=2,4 supermultiplets corresponding to the simplest chiral primary operators. These are applied to two, three and four point correlation functions. When $\N=4$, results are obtained for…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
A widely used technique for improving policies is success conditioning, in which one collects trajectories, identifies those that achieve a desired outcome, and updates the policy to imitate the actions taken along successful trajectories.…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of…
We introduce a technique to estimate a linear operator by embedding it in a family $A_t$ of operators, $t\in(\sigma_0,\infty)$, with suitable curvature properties. One can then estimate the norm of each $A_t$ by bounds that hold in the…
We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost. The utility function considered is…
As discussed in previous studies, the efficacy of evolutionary or reinforcement learning algorithms for continuous control optimization can be enhanced by including a neural module dedicated to feature extraction trained through…
We have previously developed a polymer-like expansion that applies when the (effective) action in a functional integral is an analytic function of the fields being integrated. Here, we develop methods to aid the application of this…
In this article we study the asymptotic behavior of solutions of some fractional differential equations. We prove convergence to power type functions under some assumptions on the nonlinearities. Our results extend and generalize some…
We extend the asymptotic Samuel function of an ideal to a filtration and show that many of the good properties of this function for an ideal are true for filtrations. There are, however, interesting differences, which we explore. We study…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
We consider the asymptotic evaluation of the integral transform $\int_0^\infty f(x) \, \sin^n(\lambda x)/x^n \,\text{d} x$ of an exponential type function $f(x)$ of type $\tau>0$, for large values of the parameter $\lambda$, where $n$ is a…