Related papers: Strategies for Asymptotic Normalization

We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a Wiener process) multiplied by a possibly degenerate…

We study randomly stopped sums via their asymptotic scales. First, finiteness of moments is considered. To generalise this study, asymptotic scales applicable to the class of all heavy-tailed random variables are used. The stopping is…

We develop symbolic methods of asymptotic approximations for solutions of linear ordinary differential equations and use to them stabilize numerical calculations. Our method follows classical analysis for first-order systems and…

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…

We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…

Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…

This paper investigates asymptotic behaviors of gradient descent algorithms (particularly accelerated gradient descent and stochastic gradient descent) in the context of stochastic optimization arising in statistics and machine learning…

We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…

We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is a non-trivial adaptation of the reducibility…

Recurrence quantification analysis is a method for measuring the complexity of dynamical systems. Recurrence determinism is a fundamental characteristic of it, closely related to correlation sum. In this paper, we study asymptotic behavior…

In this paper we prove that any lambda-term that is strongly normalising for beta-reduction is also strongly normalising for beta,assoc-reduction. assoc is a call-by-value rule that has been used in works by Moggi, Joachimsky, Espirito…

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…

We consider two independent random variables with the given tail asymptotic (e.g. power or exponential). We find tail asymptotic for their sum and product. This is done by some cumbersome but purely technical computations and requires the…

Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…

We study the asymptotic behaviour of additive functionals of random walks in random scenery. We establish bounds for the moments of the local time of the Kesten and Spitzer process.These bounds combined with a previous moment convergence…

We consider a general problem of finding a strategy that minimizes the exponential moment of a given cost function, with an emphasis on its relation to the more common criterion of minimization the expectation of the first moment of the…

A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…

We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…

We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a…