Sample Path Analysis and Distributions of Boundary Crossing Times

  • Shelemyahu Zacks

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

  • Shelemyahu Zacks
    • 1
  1. 1.Binghamton UniversityBinghamtonUSA

Bibliographic information