© 2017

Sample Path Analysis and Distributions of Boundary Crossing Times


Part of the Lecture Notes in Mathematics book series (LNM, volume 2203)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Shelemyahu Zacks
    Pages 1-2
  3. Shelemyahu Zacks
    Pages 3-10
  4. Shelemyahu Zacks
    Pages 11-39
  5. Shelemyahu Zacks
    Pages 41-67
  6. Shelemyahu Zacks
    Pages 69-85
  7. Shelemyahu Zacks
    Pages 87-96
  8. Shelemyahu Zacks
    Pages 97-99
  9. Shelemyahu Zacks
    Pages 101-110
  10. Shelemyahu Zacks
    Pages 111-119
  11. Back Matter
    Pages 121-135

About this book


This monograph is focused on the derivations of exact distributions of first boundary crossing times of Poisson processes, compound Poisson processes, and more general renewal processes.  The content is limited to the distributions of first boundary crossing times and their applications to various stochastic models. This book provides the theory and techniques for exact computations of distributions and moments of level crossing times. In addition, these techniques could replace simulations in many cases, thus providing more insight about the phenomenona studied.

This book takes a general approach for studying telegraph processes and is based on nearly thirty published papers by the author and collaborators over the past twenty five years.  No prior knowledge of advanced probability is required, making the book widely available to students and researchers in applied probability, operations research, applied physics, and applied mathematics. 


Poisson Processes Compound Poisson Processes Renewal Processes Compound Renewal Processes Brownian Motions Telegraph Processes Distributions of First Crossing Times Applications in Queueing Inventory and Sequential Analysis Probability Theory and Stochastic Processes Operations Research Management Science

Authors and affiliations

  1. 1.Binghamton UniversityBinghamtonUSA

About the authors

Shelemyahu Zacks is an Emeritus Distinguished Research Professor in the SUNY system. He received his Ph.D. at Columbia University, New York, in 1962. He did his post- doctoral research at Stanford University.  From 1963 till 2014 he had an academic career at several universities. He published nine books and close to 200 papers in best refereed journals in the areas of Mathematical Statistics and Applied Probability. He had thirty doctoral students. He was Chief Editor of the Journal of Statistical Planning and Inference (JSPI) and Associate Editor of several other journals of statistics and probability. Professor Zacks is Fellow of the IMS, ASA, AAAS and Elected Member of the ISI.  

Bibliographic information

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