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Applied Probability Models with Optimization Applications (Dover Books on Mathematics)

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Applied Probability Models with Optimization Applications (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

Concise advanced-level introduction to stochastic processes that frequently arise in applied probability. Largely self-contained text covers Poisson process, renewal theory, Markov chains, inventory theory, Brownian motion and continuous time optimization models, much more. Problems and references at chapter ends. "Excellent introduction." — Journal of the American Statistical Association. Bibliography. 1970 edition.

Synopsis:

Concise advanced-level introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more. Problems. References. Bibliography. 1970 edition.

Table of Contents

1. INTRODUCTION TO STOCHASTIC PROCESSES

  1.1. Random Variables and Probability Theory

  1.2. Conditional Expectation

  1.3. Stochatic Processes

    Problems

2. THE POISSON RPCESS

  2.1 Introduction and Definitions

  2.2 Interarrival and Waiting Time Distributions

  2.3 Conditional Distribution of the Arrival Times

  2.4 Compound and Nonhomogenous Poisson Processes

  2.5 Stationary Point Processes

    Problems

    References

3. RENEWAL THEORY

  3.1 Introduction and Preliminaries

  3.2 Renewal Equation and Generalizations

  3.3 Limit Theorems

  3.4 Wald's Equation

  3.5 Back to Renewal Theory

  3.6 Excess Life and Age Distribution

  3.7 Delayed Renewal Processes

  3.8 Counter Models

  3.9 Renewal Reward Process

  3.10 Nonterminating versus Terminating Renewal Processes

  3.11 Age Dependent Branching Processes

    Problems

    References

4. MARKOV CHAINS

  4.1 Preliminaries and Examples

  4.2 Classification of States

  4.3 Limit Theorems

  4.4 Transitions Among Classes

  4.5 Branching Processes

  4.6 Transient States

    Problems

    References

5. "SEMI-MARKOV, MARKOV RENEWAL AND REGERNERATIVE PROCESSES"

  5.1 Introduction and Preliminaries

  5.2 Classification of States

  5.3 Some Simple Relationships

  5.4 Regenerative Processes

  5.5 A Queueing Application

  5.6 Back to Markov Renewal Processes-Limiting Probabilities

  5.7 Limiting Distributions of the Markov Renewal Process

  5.8 Continuous Time Markov Chains

  5.9 Birth and Death Processes

    Problems

    References

6. MARKOV DECISION PROCESSES

  6.1 Introduction

  6.2 Expected Discounted Cost

  6.3 Some Examples

  6.4 "Positive Costs, No Discounting"

  6.5 Applications: Optimal Stopping and Sequential Analysis

  6.6 Expected Average Cost Criterion-Introduction and Counter examples

  6.7 Expected Average Cost Criterion

  6.8 Finite State Space-Computational Approaches

    Problems

    References

7. SEMI-MARKOV DECISION PROCESSES

  7.1 Introduction

  7.2 Discounted Cost Criterion

  7.3 Average Cost-Preliminaries and Equality of Criteria

  7.4 Average Cost-Results

  7.5 Some Examples

    Problems

    References

8. INVENTORY THEORY

  8.1 Introduction

  8.2 A Single Period Model

  8.3 Multi-Period Models

  8.4 A Multi-Period Stationary Optimal Policy

  8.5 Inventory Issuing Policies

    Problems

    References

9. BROWNIAN MOTION AND CONTINUOUS TIME OPTIMIZATION MODELS

  9.1 Introduction and Preliminaries

  9.2 Maximum of the Wiener Process

  9.3 The Wiener Process and Optimization

  9.4 The Maximum Variable-A Renewal Application

  9.5 Optimal Dispatching of a Poisson Process

  9.6 Infinitesimal Look-Ahead Stopping Rules

    Problems

    Reference

  APPENDICES

  INDEX

Product Details

ISBN:
9780486673141
Author:
Ross, Sheldon M.
Publisher:
Dover Publications
Author:
Mathematics
Subject:
Mathematics
Subject:
Mathematical Analysis
Subject:
Statistics
Subject:
Probability
Subject:
Probabilities
Subject:
Mathematical optimization
Subject:
Probability & Statistics - General
Subject:
General Mathematics
Subject:
Mathematics | Probability and Statistics
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
19921231
Binding:
TRADE PAPER
Language:
English
Pages:
224
Dimensions:
8.5 x 5.38 in 0.53 lb

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Related Subjects


Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Modeling
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Probability Theory
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Applied Probability Models with Optimization Applications (Dover Books on Mathematics) New Trade Paper
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Product details 224 pages Dover Publications - English 9780486673141 Reviews:
"Synopsis" by ,
Concise advanced-level introduction to stochastic processes that arise in applied probability. Poisson process, renewal theory, Markov chains, Brownian motion, much more. Problems. References. Bibliography. 1970 edition.

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