Asymptotic Properties of Multicolor Randomly Reinforced Pólya Urns

The generalized Pólya urn has been extensively studied and is widely applied in many disciplines. An important application of urn models is in the development of randomized treatment allocation schemes in clinical studies. The randomly reinforced urn was recently proposed, but, although the model has some intuitively desirable properties, it lacks theoretical justification. In this paper we obtain important asymptotic properties for multicolor reinforced urn models. We derive results for the rate of convergence of the number of patients assigned to each treatment under a set of minimum required conditions and provide the distributions of the limits. Furthermore, we study the asymptotic behavior for the nonhomogeneous case.

Download Full-text

ASYMPTOTIC PROPERTIES OF KOLMOGOROV WIDTHS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972710000043 ◽

2010 ◽

Vol 82 (1) ◽

pp. 10-17

Author(s):

MIKHAIL I. OSTROVSKII

Keyword(s):

Banach Space ◽

Asymptotic Behavior ◽

Banach Spaces ◽

Asymptotic Properties ◽

Codimension One ◽

Kolmogorov Widths

AbstractWe consider two problems concerning Kolmogorov widths of compacts in Banach spaces. The first problem is devoted to relations between the asymptotic behavior of the sequence of n-widths of a compact and of its projections onto a subspace of codimension one. The second problem is devoted to comparison of the sequence of n-widths of a compact in a Banach space 𝒴 and of the sequence of n-widths of the same compact in other Banach spaces containing 𝒴 as a subspace.

Download Full-text

Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments

Abstract and Applied Analysis ◽

10.1155/2013/748683 ◽

2013 ◽

Vol 2013 ◽

pp. 1-20 ◽

Cited By ~ 4

Author(s):

Justine Yasappan ◽

Ángela Jiménez-Casas ◽

Mario Castro

Keyword(s):

Asymptotic Behavior ◽

Viscoelastic Fluid ◽

Closed Loop ◽

Theoretical Study ◽

Equations Of Motion ◽

Asymptotic Properties ◽

Inertial Manifold ◽

Thermal Gradients ◽

External Temperature ◽

First Time

Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient.

Download Full-text

Limit Theory for High Frequency Sampled MCARMA Models

Advances in Applied Probability ◽

10.1239/aap/1409319563 ◽

2014 ◽

Vol 46 (3) ◽

pp. 846-877 ◽

Cited By ~ 3

Author(s):

Vicky Fasen

Keyword(s):

Asymptotic Behavior ◽

High Frequency ◽

Lévy Process ◽

Asymptotic Properties ◽

Domain Of Attraction ◽

Levy Process ◽

Sample Variance ◽

Limit Theory ◽

Second Moments ◽

Time Grid

We consider a multivariate continuous-time ARMA (MCARMA) process sampled at a high-frequency time grid {hn, 2hn,…, nhn}, where hn ↓ 0 and nhn → ∞ as n → ∞, or at a constant time grid where hn = h. For this model, we present the asymptotic behavior of the properly normalized partial sum to a multivariate stable or a multivariate normal random vector depending on the domain of attraction of the driving Lévy process. Furthermore, we derive the asymptotic behavior of the sample variance. In the case of finite second moments of the driving Lévy process the sample variance is a consistent estimator. Moreover, we embed the MCARMA process in a cointegrated model. For this model, we propose a parameter estimator and derive its asymptotic behavior. The results are given for more general processes than MCARMA processes and contain some asymptotic properties of stochastic integrals.

Download Full-text

Steepest descent evolution equations: asymptotic behavior of solutions and rate of convergence

Transactions of the American Mathematical Society ◽

10.1090/s0002-9947-99-02508-8 ◽

1999 ◽

Vol 351 (12) ◽

pp. 4847-4860 ◽

Cited By ~ 7

Author(s):

R. Cominetti ◽

O. Alemany

Keyword(s):

Asymptotic Behavior ◽

Rate Of Convergence ◽

Evolution Equations ◽

Steepest Descent ◽

Asymptotic Behavior Of Solutions

Download Full-text

The Prospects of Succinates’ Use under Hypoxic Conditions in COVID-19

Antibiotics and Chemotherapy ◽

10.37489/0235-2990-2021-66-1-2-65-74 ◽

2021 ◽

Vol 66 (1-2) ◽

pp. 65-74

Author(s):

Yu. Р. Orlov ◽

V. V. Afanasyev ◽

I. A. Khilenko

Keyword(s):

Clinical Studies ◽

Multiple Organ ◽

Tissue Hypoxia ◽

Diaphragmatic Dysfunction ◽

Pathogenetic Role ◽

Domestic Literature ◽

Hypoxic Conditions ◽

Number Of Patients ◽

Positive Effect

The aim of the work was the search for materials from experimental and clinical studies reflecting the pathogenetic role of the possible use of succinates for the correction of hypoxia in COVID-19. Materials and methods. 79 foreign and domestic literature sources were analyzed concerning the pathogenesis of COVID-19 and the pathogenetic role of succinates in hypoxia under conditions of COVID-19, oxidative stress, and diaphragmatic dysfunction were analyzed. The literature search was carried out using Pubmed and ELIBRARY.ru databases. Results. As the analysis of the literature has shown, tissue hypoxia is the basis of COVID-19 pathogenesis, triggering the entire cascade of pathomorphological events leading to the development of multiple organ failure. A number of experimental and clinical studies (on a fairly large number of patients) reflect the positive effect of tissue hypoxia correction using succinates, both in adult patients and in children with a different spectrum of pathology associated with acute respiratory failure syndrome. Conclusion. Analysis of literature data allows to substantiate the prospect of using preparations containing succinate (reamberin, cytoflavin) in the complex therapy of severe cases of COVID-19.

Download Full-text

With Jumps: An Introduction to Power Variations

High-Frequency Financial Econometrics ◽

10.23943/princeton/9780691161433.003.0004 ◽

2014 ◽

Author(s):

Yacine Aïıt-Sahalia ◽

Jean Jacod

Keyword(s):

Asymptotic Behavior ◽

Rate Of Convergence ◽

Method Of Moments ◽

Generalized Method Of Moments ◽

Parametric Estimation ◽

Continuous Part ◽

Moment Functions ◽

The Law

This chapter studies the simplest possible process having both a non-trivial continuous part and jumps. It starts with the asymptotic behavior of power variations when the model is nonparametric, that is, without specifying the law of the jumps. This is done in the same spirit as in Chapter 3: the ideas for the proofs are explained in detail, but technicalities are omitted. Then, it considers the use of these variations in a parametric estimation setting based on the generalized method of moments. There, it considers the ability of certain moment functions, corresponding to power variations, to achieve identification of the parameters of the model and the resulting rate of convergence. It shows that the general nonparametric results have a parametric counterpart in terms of which values of the power p are better able to identify parameters from either the continuous or jump part of the model.

Download Full-text

A PROOF OF ANDREWS’ CONJECTURE ON PARTITIONS WITH NO SHORT SEQUENCES

Forum of Mathematics Sigma ◽

10.1017/fms.2019.8 ◽

2019 ◽

Vol 7 ◽

Author(s):

DANIEL M. KANE ◽

ROBERT C. RHOADES

Keyword(s):

Asymptotic Behavior ◽

Modular Form ◽

Generating Function ◽

Generating Functions ◽

Asymptotic Properties ◽

Bootstrap Percolation ◽

Asymptotic Result ◽

Integer Partitions ◽

Mock Modular Form ◽

Precise Asymptotic

Our main result establishes Andrews’ conjecture for the asymptotic of the generating function for the number of integer partitions of$n$without$k$consecutive parts. The methods we develop are applicable in obtaining asymptotics for stochastic processes that avoid patterns; as a result they yield asymptotics for the number of partitions that avoid patterns.Holroyd, Liggett, and Romik, in connection with certain bootstrap percolation models, introduced the study of partitions without$k$consecutive parts. Andrews showed that when$k=2$, the generating function for these partitions is a mixed-mock modular form and, thus, has modularity properties which can be utilized in the study of this generating function. For$k>2$, the asymptotic properties of the generating functions have proved more difficult to obtain. Using$q$-series identities and the$k=2$case as evidence, Andrews stated a conjecture for the asymptotic behavior. Extensive computational evidence for the conjecture in the case$k=3$was given by Zagier.This paper improved upon early approaches to this problem by identifying and overcoming two sources of error. Since the writing of this paper, a more precise asymptotic result was established by Bringmann, Kane, Parry, and Rhoades. That approach uses very different methods.

Download Full-text

Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type

Discrete Dynamics in Nature and Society ◽

10.1155/2018/2368694 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Janusz Migda ◽

Małgorzata Migda ◽

Magdalena Nockowska-Rosiak

Keyword(s):

Asymptotic Behavior ◽

Difference Equations ◽

Existence Of Solutions ◽

Asymptotic Properties ◽

Sufficient Conditions ◽

Type Equation ◽

Asymptotic Behavior Of Solutions ◽

Volterra Type ◽

Order Difference ◽

Prescribed Asymptotic Behavior

We consider the discrete Volterra type equation of the form Δ(rnΔxn)=bn+∑k=1nK(n,k)f(xk). We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use o(ns), for given nonpositive real s, as a measure of approximation.

Download Full-text