Comparison Methods for Stochastic Models and Risks

Stochastic order relations prprovide a valuable insight into the behaviour of complex stochastic (random) systems and enable the user to collect meaningful comparative data. Application areas include queueing systems, actuarial and financial risk, decision making and stochastic simulation.
* Applicable to a broad range of scientific disciplines, including economics, finance, insurance and operations research
* Provides coverage of the latest research and applications
An essential resource for researchers and postgraduate students appliying stochastic order relations, and scientisits from applied statistics, operations research, economics and finance.Stochastische Ordnungsbeziehungen geben Aufschlüsse über das Verhalten komplexer stochastischer (zufälliger) Systeme und ermöglichen die Zusammenstellung signifikanter Vergleichsdaten. Zu den Anwendungsgebieten gehören die Organisation von Warteschlangen-Systemen (Queueing), die Abschätzung von Versicherungs- und Finanzrisiken, die Entscheidungstheorie und die stochastische Simulation, eingesetzt in den verschiedensten Wissenschaftsbereichen (Ökonomie, Finanzwirtschaft, Versicherungen, Operations-Research). Dieser Band faßt für Sie die neueste Forschungsergebnisse auf diesem Gebiet und aktuelle Anwendungen stochastischer Modelle zusammen. Preface.

Univariate Stochastic Orders

Theory of Integral Stochastic Orders

Multivariate Stochastic Orders

Stochastic Models, Comparison and Monotonicity

Monotonicity and Comparability of Stochastic Processes

Monotonicity Properties and Bounds for Queueing Systems

Applications to Various Stochastic Models

Comparing Risks.

List of Symbols.

References.

Index. "…a noteworthy contribution to applied probability, and I would recommend it to anyone interested in applied stochastic modeling." (Journal of the American Statistical Association, June 2005)

“…will replace the excellent but now slightly dated text by Shaked and Shathikumar (1994) as the standard reference on stochastic orders.” (Statistical Papers, Vol.46, No.1, January 2005)

"...provides an up-to-date survey of a notable area..." (Mathematical Reviews, 2003d)

"...discusses the major concepts related to stochastic orders..." (SciTech Book News, Vol. 26, No. 2, June 2002)

"...a very timely and methodically orientated book..." (Zentralblatt Math, Vol.999, No.24, 2002)

Alfred Müller is the author of Comparison Methods for Stochastic Models and Risks, published by Wiley. Dietrich Stoyan is a mathematician and statistician. He was a student of Mathematics at Technical University Dresden and of applied research at Deutsches Brennstoffinstitut Freiberg. Stochastic orders are important approximation tools that provide valuable insight into the behaviour of complex stochastic models. Research into stochastic orders is blossoming, with many open problems being studied and a wide range of applications explored. In this book the authors explore the most important concepts of the field, from the basic univariate theory through to the most current applications.
* Comprehensive coverage of the theory and applications of stochastic orders.

* Employs a systematic approach with detailed explanation of each concept.

* Features coverage of univariate and multivariate stochastic orders.

* Covers a range of applications, from queueing theory, reliability theory, statistical physics, actuarial and financial risk, and economics.

* Written by authors with many years experience in researching stochastic orders.
Researchers and graduate students studying stochastic orders will find the comprehensive coverage of the subject ideal for their needs. The range of applications will benefit those working in applied probability and statistics, reliability, actuarial science, economics and finance.