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2703 results in General statistics and probability

Page 19 of 136

Stable Lévy Processes via Lamperti-Type Representations
  • Andreas E. Kyprianou, Juan Carlos Pardo
  • Published online:
    16 March 2022
    Print publication:
    07 April 2022
  • Stable Lévy processes lie at the intersection of Lévy processes and self-similar Markov processes. Processes in the latter class enjoy a Lamperti-type representation as the space-time path transformation of so-called Markov additive processes (MAPs). This completely new mathematical treatment takes advantage of the fact that the underlying MAP for stable processes can be explicitly described in one dimension and semi-explicitly described in higher dimensions, and uses this approach to catalogue a large number of explicit results describing the path fluctuations of stable Lévy processes in one and higher dimensions. Written for graduate students and researchers in the field, this book systemically establishes many classical results as well as presenting many recent results appearing in the last decade, including previously unpublished material. Topics explored include first hitting laws for a variety of sets, path conditionings, law-preserving path transformations, the distribution of extremal points, growth envelopes and winding behaviour.

Computer Age Statistical Inference, Student Edition
  • Algorithms, Evidence, and Data Science
  • Bradley Efron, Trevor Hastie
  • Published online:
    26 October 2021
    Print publication:
    17 June 2021
  • The twenty-first century has seen a breathtaking expansion of statistical methodology, both in scope and influence. 'Data science' and 'machine learning' have become familiar terms in the news, as statistical methods are brought to bear upon the enormous data sets of modern science and commerce. How did we get here? And where are we going? How does it all fit together? Now in paperback and fortified with exercises, this book delivers a concentrated course in modern statistical thinking. Beginning with classical inferential theories - Bayesian, frequentist, Fisherian - individual chapters take up a series of influential topics: survival analysis, logistic regression, empirical Bayes, the jackknife and bootstrap, random forests, neural networks, Markov Chain Monte Carlo, inference after model selection, and dozens more. The distinctly modern approach integrates methodology and algorithms with statistical inference. Each chapter ends with class-tested exercises, and the book concludes with speculation on the future direction of statistics and data science.

  • 12 - Processing Networks and Maximum Pressure Policies

  • from Part IV - Fluid Models of Multi-Class Queueing
  • Gideon Weiss, University of Haifa, Israel
  • Book:
    Scheduling and Control of Queueing Networks
    Published online:
    01 October 2021
    Print publication:
    14 October 2021, pp 197-218

  • Summary

    We introduces some more general processing networks and the maximum pressure policy, which uses local information for decentralized control of the network. Maximum pressure policies can guarantee the stability of MCQN as well as of more general processing networks, under some simple structure conditions, whenever traffic intensity rho < 1.

  • 4 - The G/G/1 Queue

  • from Part II - Approximations of the Single Queue
  • Gideon Weiss, University of Haifa, Israel
  • Book:
    Scheduling and Control of Queueing Networks
    Published online:
    01 October 2021
    Print publication:
    14 October 2021, pp 61-70

  • Summary

    We present the ingenious scheme devised by Loynes to show that G/G/1 with stationary arrival and service processes is stable when the traffic intensity rho < 1, and transient if rho > 1. Under the stronger assumption that interarrivals and services are i.i.d., we explore the connection of the GI/GI/1 queue with the general random walk and obtain an insightful upper bound on waiting time.

  • 9 - Generalized Jackson Networks

  • from Part III - Queueing Networks
  • Gideon Weiss, University of Haifa, Israel
  • Book:
    Scheduling and Control of Queueing Networks
    Published online:
    01 October 2021
    Print publication:
    14 October 2021, pp 143-156

  • Summary

    We discuss the classic Jackson network with general i.i.d. interarrivals and service times, the generalized Jackson network. Like the GI/GI/1 system, the generalized Jackson network cannot be analyzed in detail, and we discuss fluid and diffusion approximations to the network process.

Page 19 of 136