Sample Path Analysis and Distributions of Boundary Crossing Times

1. Front Matter

   Pages i-xiii

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2. Introduction

   • Shelemyahu Zacks

   Pages 1-2

3. Technical Prerequisites

   • Shelemyahu Zacks

   Pages 3-10

4. First Crossing by Poisson Processes

   • Shelemyahu Zacks

   Pages 11-39

5. First Crossing by Compound Poisson Processes

   • Shelemyahu Zacks

   Pages 41-67

6. Telegraph Processes

   • Shelemyahu Zacks

   Pages 69-85

7. Sequential Estimation

   • Shelemyahu Zacks

   Pages 87-96

8. First Crossing a Random Process

   • Shelemyahu Zacks

   Pages 97-99

9. Failure Times of Deterioration Processes

   • Shelemyahu Zacks

   Pages 101-110

10. Miscellaneous Topics

    • Shelemyahu Zacks

    Pages 111-119

11. Back Matter

    Pages 121-135

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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

• Binghamton University, Binghamton, USA

  Shelemyahu Zacks

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.  

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