Stochastic Storage Processes

Stochastic Storage Processes PDF
Author: N.U. Prabhu
Publisher: Springer Science & Business Media
ISBN: 1461217423
Size: 40.78 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 207
View: 3600

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A self-contained treatment of stochastic processes arising from models for queues, insurance risk, and dams and data communication, using their sample function properties. The approach is based on the fluctuation theory of random walks, L vy processes, and Markov-additive processes, in which Wiener-Hopf factorisation plays a central role. This second edition includes results for the virtual waiting time and queue length in single server queues, while the treatment of continuous time storage processes is thoroughly revised and simplified. With its prerequisite of a graduate-level course in probability and stochastic processes, this book can be used as a text for an advanced course on applied probability models.

Stochastic Storage Processes

Stochastic Storage Processes PDF
Author: Narahari U. Prabhu
Publisher: Springer Science & Business Media
ISBN: 1468401130
Size: 73.56 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 140
View: 7144

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This book is based on a course I have taught at Cornell University since 1965. The primary topic of this course was queueing theory, but related topics such as inventories, insurance risk, and dams were also included. As a text I used my earlier book, Queues and Inventories (John Wiley, New York, 1965). Over the years the emphasis in this course shifted from detailed analysis of probability models to the study of stochastic processes that arise from them, and the subtitle of the text, "A Study of Their Basic Stochastic Processes," became a more appropriate description of the course. My own research into the fluctuation theory for U:vy processes provided a new perspective on the topics discussed, and enabled me to reorganize the material. The lecture notes used for the course went through several versions, and the final version became this book. A detailed description of my approach will be found in the Introduction. I have not attempted to give credit to authors of individual results. Readers interested in the historical literature should consult the Selected Bibliography given at the end of the Introduction. The original work in this area is presented here with simpler proofs that make full use of the special features of the underlying stochastic processes. The same approach makes it possible to provide several new results. Thanks are due to Kathy King for her excellent typing of the manuscript.

Useful Martingales For Stochastic Storage Processes With L Vy Type Input

Useful Martingales for Stochastic Storage Processes with L  vy Type Input PDF
Author:
Publisher:
ISBN:
Size: 64.31 MB
Format: PDF, Mobi
Category :
Languages : en
Pages :
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Abstract : In this paper we generalize the martingale of Kella and Whitt to the setting of Lévy-type processes and show that the (local) martingales obtained are in fact square-integrable martingales which upon dividing by the time index converge to zero almost surely and in L 2 . The reflected Lévy-type process is considered as an example.

Stochastic Storage Processes With Multiple Slope Linear Inputs And Outputs

Stochastic Storage Processes with Multiple Slope Linear Inputs and Outputs PDF
Author: Stanford University. Department of Statistics
Publisher:
ISBN:
Size: 23.92 MB
Format: PDF, ePub, Mobi
Category : Probabilities
Languages : en
Pages : 67
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Let X(t) be the level of the storage process at time t; X(0) = 0. Starting at time 0, the level X(t) increases linearly with slope s sub i for a random length of time (the input period) after which it decreases linearly with slope g sub j for a random time (the output period). Subsequently, the process continues to alternate between periods of input and output where the input-output transitions are governed by a transition matrix P, and the output-input transitions by Q. For each input slope i and output slope j, there corresponds an input period distribution F sub i and an output period distribution M sub j which is exponential. When the zero level is a positive recurrent state, the steady state joint distributions of the level of the process and the slope is obtained. The means of these distributions are determined. The mean nonempty period is also determined. When the zero level is a transient state, the limiting distribution of the storage level is obtained.

Stochastic Process Limits

Stochastic Process Limits PDF
Author: Ward Whitt
Publisher: Springer Science & Business Media
ISBN: 0387217487
Size: 65.69 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 602
View: 3724

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From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews

Stochastic Processes

Stochastic Processes PDF
Author: D. N. Shanbhag
Publisher: Gulf Professional Publishing
ISBN: 9780444500144
Size: 51.41 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 967
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J. Neyman, one of the pioneers in laying the foundations of modern statistical theory, stressed the importance of stochastic processes in a paper written in 1960 in the following terms: Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research, if treated realistically, does not involve operations on stochastic processes. Arising from the need to solve practical problems, several major advances have taken place in the theory of stochastic processes and their applications. Books by Doob (1953; J. Wiley and Sons), Feller (1957, 1966; J. Wiley and Sons) and Loeve (1960; D. van Nostrand and Col., Inc.) among others, have created growing awareness and interest in the use of stochastic processes in scientific and technological studies.The literature on stochastic processes is very extensive and is distributed in several books and journals.

Introduction To Stochastic Models

Introduction to Stochastic Models PDF
Author: Marius Iosifescu
Publisher: John Wiley & Sons
ISBN: 1118623525
Size: 23.96 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 320
View: 3985

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This book provides a pedagogical examination of the way in which stochastic models are encountered in applied sciences and techniques such as physics, engineering, biology and genetics, economics and social sciences. It covers Markov and semi-Markov models, as well as their particular cases: Poisson, renewal processes, branching processes, Ehrenfest models, genetic models, optimal stopping, reliability, reservoir theory, storage models, and queuing systems. Given this comprehensive treatment of the subject, students and researchers in applied sciences, as well as anyone looking for an introduction to stochastic models, will find this title of invaluable use.

Stochastic Portfolio Theory

Stochastic Portfolio Theory PDF
Author: E. Robert Fernholz
Publisher: Springer Science & Business Media
ISBN: 9780387954059
Size: 75.25 MB
Format: PDF, Kindle
Category : Business & Economics
Languages : en
Pages : 178
View: 1865

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Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the distributional component of portfolio return. This book is an introduction to stochastic portfolio theory for investment professionals and for students of mathematical finance. Each chapter includes a number of problems of varying levels of difficulty and a brief summary of the principal results of the chapter, without proofs.

Heavy Traffic Analysis Of Controlled Queueing And Communication Networks

Heavy Traffic Analysis of Controlled Queueing and Communication Networks PDF
Author: Harold Kushner
Publisher: Springer Science & Business Media
ISBN: 9780387952642
Size: 53.93 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 515
View: 1275

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One of the first books in the timely and important area of heavy traffic analysis of controlled and uncontrolled stochastics networks, by one of the leading authors in the field. The general theory is developed, with possibly state dependent parameters, and specialized to many different cases of practical interest.

Stochastic Analysis Of Computer Storage

Stochastic Analysis of Computer Storage PDF
Author: O.I. Aven
Publisher: Springer Science & Business Media
ISBN: 0585273731
Size: 74.11 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 254
View: 630

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Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Fother 'The Hennit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van GWs The Chinese More Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Stochastic And Statistical Methods In Hydrology And Environmental Engineering Stochastic And Statistical Modelling With Groundwater And Surface Water Applications

Stochastic and Statistical Methods in Hydrology and Environmental Engineering  Stochastic and statistical modelling with groundwater and surface water applications PDF
Author: Keith W. Hipel
Publisher: Springer Science & Business Media
ISBN: 9780792327578
Size: 66.81 MB
Format: PDF
Category : Science
Languages : en
Pages : 372
View: 4801

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World renowned scientists present valuable contributions to stochastic and statistical modelling of groundwater and surface water systems. The philosophy of probabilistic modelling in the hydrological sciences is put into proper perspective and the importance of stochastic differential equations in the environmental sciences is explained and illustrated. The new research ideas put forward in groundwater modelling will assist decision makers in tackling challenging problems such as controlling pollution of underground aquifers and obtaining adequate water supplies. Additionally, different types of stochastic models are used in modelling a range of interesting surface water problems. Other topics covered in this landmark volume include stochastic optimization, moment analysis, carbon dioxide modelling and rainfall prediction. Audience The book is of interest to researchers, teachers, students and practitioners who wish to be at the leading edge of stochastic and statistical modelling in the environmental sciences.