Bounds For Moments Research Articles

Bounds for moments of Dirichlet L-functions to a fixed modulus

Bounds for moments of Dirichlet L-functions to a fixed modulus

Bounds for moments of $$\ell $$-torsion in class groups

Bounds for moments of $$\ell $$-torsion in class groups

Lower Bounds for Moments of Quadratic Twisted Self-dual GL(3) Central L-values

Lower Bounds for Moments of Quadratic Twisted Self-dual GL(3) Central L-values

Lower Bounds for Higher Moments of the Twisted L-functions

Let f be a cuspidal holomorphic or Maass Hecke eigenform for the modular group $$\text{SL}_{2}(\mathbb{Z})$$ . Let $$L(s,f\otimes\chi)$$ denote the twisted L-function associated to f twisted by a primitive Dirichlet character χ modulo q. In this paper, we obtain a lower bound for the 2kth moment of central values of the twisted L-functions.

Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli

In this paper, we study the $k$-th moment of central values of the family of quadratic Dirichlet $L$-functions of moduli $8p$, with $p$ ranging over odd primes. Assuming the truth of the generlized Riemann hypothesis, we establish sharp upper and lower bounds for the $k$-th power moment of these $L$-values for all real $k \geq 0$.

Moment Bounds for a Generalized Anderson Model with Gaussian Noise Rough in Space

Moment Bounds for a Generalized Anderson Model with Gaussian Noise Rough in Space

Functional Correlation Bounds and Optimal Iterated Moment Bounds for Slowly-Mixing Nonuniformly Hyperbolic Maps

Consider a nonuniformly hyperbolic map T:Mrightarrow M modelled by a Young tower with tails of the form O(n^{-beta }) , beta >2 . We prove optimal moment bounds for Birkhoff sums sum _{i=0}^{n-1}vcirc T^i and iterated sums sum _{0le i<j<n}vcirc T^i, wcirc T^j , where v,w:Mrightarrow {{mathbb {R}}} are (dynamically) Hölder observables. Previously iterated moment bounds were only known for beta >5. Our method of proof is as follows; (i) prove that T satisfies an abstract functional correlation bound, (ii) use a weak dependence argument to show that the functional correlation bound implies moment estimates. Such iterated moment bounds arise when using rough path theory to prove deterministic homogenisation results. Indeed, by a recent result of Chevyrev, Friz, Korepanov, Melbourne & Zhang we have convergence to an Itô diffusion for fast-slow systems of the form xk+1(n)=xk(n)+n-1a(xk(n),yk)+n-1/2b(xk(n),yk),yk+1=Tyk\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} x^{(n)}_{k+1}=x_k^{(n)}+n^{-1}a(x_k^{(n)},y_k)+n^{-1/2}b(x_k^{(n)},y_k) , \\quad y_{k+1}=Ty_k \\end{aligned}$$\\end{document}in the optimal range beta >2.

Bounds for moments of modular $L$-functions to a fixed modulus

We study the $2k$th moment of the family of twisted modular $L$-functions to a fixed prime power modulus at the central values. We establish sharp lower bounds for all real $k \geq 0$ and sharp upper bounds for $0 \leq k \leq 1$.

Loss of Memory and Moment Bounds for Nonstationary Intermittent Dynamical Systems

We study nonstationary intermittent dynamical systems, such as compositions of a (deterministic) sequence of Pomeau-Manneville maps. We prove two main results: sharp bounds on memory loss, including the "unexpected" faster rate for a large class of measures, and sharp moment bounds for Birkhoff sums and, more generally, "separately H\"older" observables.

Bounds for discrete moments of Weyl sums and applications

We prove two bounds for discrete moments of Weyl sums. The first one can be obtained using a standard approach. The second one involves an observation how this method can be improved, which leads to a sharper bound in certain ranges. The proofs both build on the recently proved main conjecture for Vinogradov's mean value theorem. We present two selected applications: First, we prove a new $k$- th derivative test for the number of integer points close to a curve by an exponential sum approach. This yields a stronger bound than existing results obtained via geometric methods, but it is only applicable for specific functions. As second application we prove a new improvement of the polynomial large sieve inequality for one-variable polynomials of degree $k \geq 4$.

Negative Moment Bounds for Stochastic Regression Models with Deterministic Trends and Their Applications to Prediction Problems

Negative Moment Bounds for Stochastic Regression Models with Deterministic Trends and Their Applications to Prediction Problems

On Lower Bounds for Variance And Moments of Unimodal Distributions

ABSTRACT: We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is given and compared favorably with a related bound for discrete unimodal distribution in literature.

Lower Bounds for Moments of ζ′(ρ)

Lower Bounds for Moments of ζ′(ρ)

A Comparison of the Moment and Factorial Moment Bounds for Discrete Random Variables

In this note, we establish the superiority of the factorial moment bound over the moment bound for nonnegative integer-valued discrete random variables. This solves a problem given earlier. We use some results from approximation theory/ numerical analysis to compare the bounds.

Mean-field Models Involving Continuous-state-dependent Random Switching: Nonnegativity Constraints, Moment Bounds, and Two-time-scale Limits

This work concerns mean-field models, which are formulated using stochastic differential equations. Different from the existing formulations, a random switching process is added. The switching process can be used to describe the random environment and other stochastic factors that cannot be explained in the usual diffusion models. The added switching component makes the formulation more realistic, but it adds difficulty in analyzing the underlying processes. Several properties of the mean-field models are provided including regularity, nonnegativity, finite moments, and continuity. In addition, the paper addresses the issue when the switching takes place an order of magnitude faster than that of the continuous state. It derives a limit that is an average with respect to the invariant measure of the switching process.

Mean-field Models Involving Continuous-state-dependent Random Switching: Nonnegativity Constraints, Moment Bounds, and Two-time-scale Limits

This work concerns mean-field models, which are formulated using stochastic differential equations. Different from the existing formulations, a random switching process is added. The switching process can be used to describe the random environment and other stochastic factors that cannot be explained in the usual diffusion models. The added switching component makes the formulation more realistic, but it adds difficulty in analyzing the underlying processes. Several properties of the mean-field models are provided including regularity, nonnegativity, finite moments, and continuity. In addition, the paper addresses the issue when the switching takes place an order of magnitude faster than that of the continuous state. It derives a limit that is an average with respect to the invariant measure of the switching process.

Bounds for Moments of the Maximum of Concomitants of Selected Order Statistics With Application

We present sharp bounds for moments of the maximum of concomitants of selected order statistics. The dependence between pair components is modeled by copulas. We use the bounds to compare some insurance premiums.

Bounds for factorial moments of discrete distributions

Bounds for factorial moments of discrete distributions

Moment Bounds for the Smoluchowski Equation and their Consequences

We prove uniform bounds on moments X_a = \sum_{m}{m^a f_m(x,t)} of the Smoluchowski coagulation equations with diffusion, valid in any dimension. If the collision propensities \alpha(n,m) of mass n and mass m particles grow more slowly than (n+m)(d(n) + d(m)), and the diffusion rate d(\cdot) is non-increasing and satisfies m^{-b_1} \leq d(m) \leq m^{-b_2} for some b_1 and b_2 satisfying 0 \leq b_2 < b_1 < \infty, then any weak solution satisfies X_a \in L^{\infty}(\mathbb{R}^d \times [0,T]) \cap L^1(\mathbb{R}^d \times [0,T]) for every a \in \mathbb{N} and T \in (0,\infty), (provided that certain moments of the initial data are finite). As a consequence, we infer that these conditions are sufficient to ensure uniqueness of a weak solution and its conservation of mass.

Upper Bounds for Exponential Moments of Hitting Times for Semi-Markov Processes

Necessary and sufficient conditions for the existence of exponential moments for hitting times for semi-Markov processes are found. These conditions and the corresponding upper bounds for exponential moments are given in terms of test-functions. Applications to hitting times for semi-Markov random walks and queuing systems illustrate the results.