文档介绍：SEMI-MARKOV RISK MODELS FOR
FINANCE, INSURANCE AND
RELIABILITY
By
JACQUES JANSSEN
Solvay Business School, Brussels, Belgium
RAIMONDO MANCA
Università di Roma “La Sapienza,” Italy
Library of Congress Control Number: 2006940397
ISBN-10: 0-387-70729-8 e-ISBN: 0-387-70730-1
ISBN-13: 978-0-387-70729-7
Printed on acid-free paper.
AMS Subject Classifications: 60K15, 60K20, 65C50, 90B25, 91B28, 91B30
© 2007 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
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Printed in the United States of America.
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Contents
Preface XV
1 Probability Tools for Stochastic Modelling 1
1 The Sample Space 1
2 Probability Space 2
3 Random Variables 6
4 Integrability, Expectation and Independence 8
5 Main Distribution Probabilities 14
The Binomial Distribution 15
The Poisson Distribution 16
The Normal (or Laplace-Gauss) Distribution 16
The Log-Normal Distribution 19
The Negative Exponential Distribution 20
The Multidimensional Normal Distribution 20
6 Conditioning (From Independence to Dependence) 22
Conditioning: Introductory Case 22
Conditioning: General Case 26
Regular Conditional Probability 30
7 Stoc