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6791 results in Communications and signal processing

Page 51 of 340

  • 3 - Large Deviation Principles for Compound Renewal Processes

  • A. A. Borovkov
  • Translated by Alexey Alimov, Steklov Institute of Mathematics, Moscow
  • Book:
    Compound Renewal Processes
    Published online:
    16 June 2022
    Print publication:
    30 June 2022, pp 90-153

  • Summary

    We study the nature of the distributions of CRPs in the large deviation zone and establish the corresponding LDPs. We clarify the relation of the distribution of a CRP with the renewal measure for the sequence {Tn, Zn}. We investigate some properties of the deviation functions of the renewal measures that appear in this problem. We prove the LDPs for the CRPs Z(t). The definition of the fundamental function is given, and we also study its properties and relations to the deviation functions. We present several results on LDPs for the process Y(t) and for Markov additive processes.

  • 4 - Large Deviation Principles for Trajectories of Compound Renewal Processes

  • A. A. Borovkov
  • Translated by Alexey Alimov, Steklov Institute of Mathematics, Moscow
  • Book:
    Compound Renewal Processes
    Published online:
    16 June 2022
    Print publication:
    30 June 2022, pp 154-224

  • Summary

    We continue the study of large deviation principles for compound renewal processes. We are mostly concerned with probabilities of large deviations of the trajectories of CRPs. We establish "partial" LDPs (local LDPs applicable only in the space of absolutely continuous functions). "Complete" LDPs are obtained under rather restrictive conditions. It proves possible to obtain LDPs for boundary crossing problems under broader conditions and with explicit deviation functional. A moderately large deviation principle for CRPs is established.

Machine Learning and Wireless Communications
  • Edited by Yonina C. Eldar, Andrea Goldsmith, Deniz Gündüz, H. Vincent Poor
  • Published online:
    16 June 2022
    Print publication:
    04 August 2022
  • How can machine learning help the design of future communication networks – and how can future networks meet the demands of emerging machine learning applications? Discover the interactions between two of the most transformative and impactful technologies of our age in this comprehensive book. First, learn how modern machine learning techniques, such as deep neural networks, can transform how we design and optimize future communication networks. Accessible introductions to concepts and tools are accompanied by numerous real-world examples, showing you how these techniques can be used to tackle longstanding problems. Next, explore the design of wireless networks as platforms for machine learning applications – an overview of modern machine learning techniques and communication protocols will help you to understand the challenges, while new methods and design approaches will be presented to handle wireless channel impairments such as noise and interference, to meet the demands of emerging machine learning applications at the wireless edge.

Compound Renewal Processes
  • A. A. Borovkov
  • Translated by Alexey Alimov
  • Published online:
    16 June 2022
    Print publication:
    30 June 2022
  • Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations.

  • 7 - Extremal Processes

  • from Part II - Emergence
  • Jayakrishnan Nair, Indian Institute of Technology, Bombay, Adam Wierman, California Institute of Technology, Bert Zwart, Stichting Centrum voor Wiskunde en Informatica (CWI), Amsterdam
  • Book:
    The Fundamentals of Heavy Tails
    Published online:
    17 May 2022
    Print publication:
    09 June 2022, pp 148-174

  • Summary

    An introduction to the emergence of heavy-tailed distributions in the context of extremal processes.Max-stable distributions are introduced, and the extremal central limit theory is presented.Further, an example of the emergence of heavy tails in the extremes of random walks is presented.

Page 51 of 340