scholarly journals LIMIT THEOREMS FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES. IV

2014 ◽  
Vol 19 (1) ◽  
pp. 66-74 ◽  
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Elliptic Curves ◽  
Limit Theorems ◽  
Limit Measure

In this paper, we prove a multidimensional limit theorem for moduli of twists of L-functions of elliptic curves. The limit measure in this theorem is defined by the characteristic transforms.

scholarly journals LIMIT THEOREMS FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES. II

2012 ◽  
Vol 17 (1) ◽  
pp. 90-99 ◽  
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Elliptic Curves ◽  
Limit Theorems ◽  
Dirichlet Character

In the paper, a limit theorem for the argument of twisted with Dirichlet character L-functions of elliptic curves with an increasing modulus of the character is proved.

scholarly journals A JOINT ELLIOTT TYPE THEOREM FOR TWISTS OF L-FUNCTIONS OF ELLIPTIC CURVES

2016 ◽  
Vol 21 (6) ◽  
pp. 752-761
Author(s):  
Virginija Garbaliauskienė ◽  
Antanas Laurinčikas
Keyword(s):  
Limit Theorem ◽  
Elliptic Curves ◽  
Analytic Functions ◽  
Type Theorem ◽  
Dirichlet Character ◽  
Probability Measures ◽  
Space Of Analytic Functions ◽  
Limit Measure ◽  
Joint Limit Theorem ◽  
Joint Limit

We consider a collection of L-functions of elliptic curves twisted by a Dirichlet character modulo q (q is a prime number), and prove for this collection a joint limit theorem for weakly convergent probability measures in the space of analytic functions as q → ∞. The limit measure is given explicitly.

scholarly journals Central and Local Limit Theorems for Numbers of the Tribonacci Triangle

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Normal Distribution ◽  
Rate Of Convergence ◽  
Limit Theorems ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Constructive Proof ◽  
The Central Limit Theorem ◽  
Local Limit Theorems

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

Heavy traffic limit theorems in fluctuation theory

1978 ◽  
Vol 10 (04) ◽  
pp. 852-866
Author(s):  
A. J. Stam
Keyword(s):  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Limit Theorems ◽  
Heavy Traffic ◽  
The Central Limit Theorem ◽  
Heavy Traffic Limit ◽  
Oscillating Random Walk

Let be a family of random walks with For ε↓0 under certain conditions the random walk U (∊) n converges to an oscillating random walk. The ladder point distributions and expectations converge correspondingly. Let M ∊ = max {U (∊) n , n ≧ 0}, v 0 = min {n : U (∊) n = M ∊}, v 1 = max {n : U (∊) n = M ∊}. The joint limiting distribution of ∊2σ∊ –2 v 0 and ∊σ∊ –2 M ∊ is determined. It is the same as for ∊2σ∊ –2 v 1 and ∊σ–2 ∊ M ∊. The marginal ∊σ–2 ∊ M ∊ gives Kingman's heavy traffic theorem. Also lim ∊–1 P(M ∊ = 0) and lim ∊–1 P(M ∊ < x) are determined. Proofs are by direct comparison of corresponding probabilities for U (∊) n and for a special family of random walks related to MI/M/1 queues, using the central limit theorem.

scholarly journals Realization of the probability laws in the quantum central limit theorems by a quantum walk

2013 ◽  
Vol 13 (5&6) ◽  
pp. 430-438
Author(s):  
Takuya Machida
Keyword(s):  
Probability Theory ◽  
Limit Theorem ◽  
Central Limit ◽  
Discrete Time ◽  
Limit Theorems ◽  
Quantum Walk ◽  
Quantum Probability ◽  
Quantum Walks ◽  
Central Limit Theorems ◽  
Initial State

Since a limit distribution of a discrete-time quantum walk on the line was derived in 2002, a lot of limit theorems for quantum walks with a localized initial state have been reported. On the other hand, in quantum probability theory, there are four notions of independence (free, monotone, commuting, and boolean independence) and quantum central limit theorems associated to each independence have been investigated. The relation between quantum walks and quantum probability theory is still unknown. As random walks are fundamental models in the Kolmogorov probability theory, can the quantum walks play an important role in quantum probability theory? To discuss this problem, we focus on a discrete-time 2-state quantum walk with a non-localized initial state and present a limit theorem. By using our limit theorem, we generate probability laws in the quantum central limit theorems from the quantum walk.

scholarly journals Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration

2017 ◽  
Vol 54 (2) ◽  
pp. 569-587 ◽  
Author(s):  
Ollivier Hyrien ◽  
Kosto V. Mitov ◽  
Nikolay M. Yanev
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Cell Populations ◽  
Subcritical Case ◽  
Immigration Process ◽  
Large Numbers

Abstract We consider a class of Sevastyanov branching processes with nonhomogeneous Poisson immigration. These processes relax the assumption required by the Bellman–Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper we focus on the subcritical case and examine asymptotic properties of the process. We establish limit theorems, which generalize classical results due to Sevastyanov and others. Our key findings include a novel law of large numbers and a central limit theorem which emerge from the nonhomogeneity of the immigration process.

Simple random walks on semi-groups of nilpotency class two

1966 ◽  
Vol 3 (01) ◽  
pp. 156-170
Author(s):  
D. C. Dowson
Keyword(s):  
Limit Theorem ◽  
Central Limit ◽  
Conditional Distribution ◽  
Limit Theorems ◽  
Good Deal ◽  
Nilpotency Class ◽  
Standard Normal Distribution ◽  
Semi Group ◽  
Bernoulli Sequence ◽  
Standard Normal

One of the earliest known distributions is that of the Binomial distribution which arises from a Bernoulli sequence defined on two symbols (or generators) a and b. The corresponding limit theorem is that of Demoivre and Laplace and states (in an obvious notation) that (r – np)/√npq converges to the standard Normal distribution N(0,1). If the generators do not commute the situation is a good deal more complicated and in order to say very much about the sequences generated we must be able to put them in some simple canonical form. One case in which this can certainly be done is when the two symbols generate a semi-group of nilpotency class two. This means that although ba ≠ ab, we do have ba = ab (b,a) where (b, a) is a symbol which commutes with both a and b. Each sequence can then be expressed in the form aαbβ (b,a) γ . In this paper we examine first the conditional distribution of γ given α and β for Bernoulli sequences in the symbols a and b and obtain central limit theorems when γ is appropriately normed. We then consider the more general problem of the m-generator semi-group of nilpotency class two and obtain the corresponding multi-dimensional central limit theorem in the case where the probability measure is discrete and is distributed over the generators.

A Poisson limit theorem for incomplete symmetric statistics

1983 ◽  
Vol 20 (01) ◽  
pp. 47-60 ◽  
Author(s):  
M. Berman ◽  
G. K. Eagleson
Keyword(s):  
Limit Theorem ◽  
Limit Theorems ◽  
Random Variables ◽  
Asymptotic Distributions ◽  
Poisson Limit ◽  
Symmetric Statistics ◽  
Limit Result ◽  
Independent Identically Distributed

Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.

scholarly journals Limit theorems for multivariate Brownian semistationary processes and feasible results

2019 ◽  
Vol 51 (03) ◽  
pp. 667-716
Author(s):  
Riccardo Passeggeri ◽  
Almut E. D. Veraart
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Laws Of Large Numbers ◽  
Stationary Increments ◽  
Large Numbers ◽  
Weak Laws

AbstractIn this paper we introduce the multivariate Brownian semistationary (BSS) process and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general multivariate Gaussian processes with stationary increments, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems, and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.

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