Related papers: Optimized Self-Similar Borel Summation

We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite variance, we show that when rescaled by $N^{1/s}(\ln N)^\alpha$,…

In bandit algorithms, the randomly time-varying adaptive experimental design makes it difficult to apply traditional limit theorems to off-policy evaluation of the treatment effect. Moreover, the normal approximation by the central limit…

This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…

In (Boyd, Proc. R. Soc. Lond. A 447 (1994) 609--630), W. G. C. Boyd derived a resurgence representation for the gamma function, exploiting the reformulation of the method of steepest descents by M. Berry and C. Howls (Berry and Howls, Proc.…

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.…

In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…

Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…

We show that a formal power series has positive radius of convergence if and only if it is uniformly Borel summable over a circle with center at the origin. Consequently, we obtain that an entire function $f$ is of exponential type if and…

We study the zero-dimensional prototype of the path integrals in quantum mechanics and quantum field theory, with the action $S(\phi)=\frac{\sigma }{2}\phi^{2}+\frac{\lambda}{4}\phi^{4}$. Using the Lefschetz thimble decomposition and the…

We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power…

Variational data assimilation technique applied to the identification of the optimal discretization of interpolation operators and derivatives in the nodes adjacent to the boundary of the domain is discussed in frames of the linear shallow…

We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional $\infty$-Laplacian $\Delta_\infty^s$ for $s\in (\frac{1}{2},1)$. This operator has been introduced and first studied in…

We generalize the notion of an asymptotic weak coupling expansion about an exactly solvable model in quantum mechanics and quantum field theory to an all positive value coupling convergent expansion. This is done by rescaling the variables…

In the present paper we derive the asymptotic expansion formula for the trapezoidal approximation of the fractional integral. We use the expansion formula to obtain approximations for the fractional integral of order…

We apply the zero bias transformation to deduce a recursive asymptotic expansion formula for expectation of functions of sum of independent random variables in terms of normal expectations and we discuss the remainder term estimations.

This paper describes three methods for carrying out non-asymptotic inference on partially identified parameters that are solutions to a class of optimization problems. Applications in which the optimization problems arise include estimation…

We develop a method that uses truncation-order-dependent re-expansions constrained by generic strong-coupling information to extrapolate perturbation series to the nonperturbative regime. The method is first benchmarked against a…

The critical behavior of two-dimensional $n$-vector $\lambda\phi^4$ field model is studied within the framework of pseudo-$\epsilon$ expansion approach. Pseudo-$\epsilon$ expansions for Wilson fixed point location $g^*$ and critical…

There are three main types of numerical computations for the Bessel function of the second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they are combined in the appropriate domain for each. However,…

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…