Stochastic Processes: Theory and Methods: SHANBHAG D. N. : 9780444500144: Book: Technology: eCampus.com

Preface

Contributors

Pareto Processes

(34)

Barry C. Arnold

Introduction

(1)

Distributional properties of Pareto variables

(2)

Multivariate Pareto distributions

(7)

Pareto processes

(1)

Autoregressive classical Pareto processes

(4)

Autoregressive Pareto (III) processes

(6)

Extensions and modifications

(5)

Related processes

(8)

References

(3)

Branching Processes

(20)

K. B. Athreya

A. N. Vidyashankar

Introduction

(1)

Branching processes Single type case

(4)

Branching process: Multitype case

(4)

Continuous time (age dependent) branching processes

(2)

Branching processes in random environments

(2)

Branching random walks

(7)

Acknowledgements

(1)

References

(5)

Inference in Stochastic Processes

(24)

I. V. Basawa

Introduction

(1)

Likelihood methods

(10)

Optimal estmating functions

(1)

Semiparametric models and adaptive estimation

(1)

Bayes and empirical Bayes methods

(1)

Some applications

(10)

Acknowledgement

(1)

References

(3)

Topics in poisson Approximation

(38)

A. D. Barbour

Introduction

(5)

The Stein-Chen method

(7)

Probabilities of small counts

(5)

Poisson point process approximation

(7)

Compound Poisson approximation

103

(14)

Acknowledgement

112

(1)

References

112

(5)

Some Elements on Levy Processes

117

(28)

Jean Bertoin

Introduction

117

(1)

Basic aspects of Levy processes

118

(9)

Distribution of some functionals

127

(8)

Some sample path properties

135

(10)

References

142

(3)

Iterated Random Maps and Some Classes of Markov Processes

145

(26)

Rabi Bhattacharya

Edward C. Waymire

Introduction

145

(9)

Ergodic problem, rates of convergence, and the central limit theorem

154

(1)

Doeblin's minorization and coupling via backward iteration

155

(2)

Harris recurrence, small sets, local minorization, and regeneration

157

(1)

Liapounov functionals and Foster-Tweedie drift conditions

158

(1)

Dubins-Freedman splitting for monotone maps and its generalization

159

(3)

Localized splitting

162

(3)

Examples revisited

165

(6)

Acknowledgements

168

(1)

References

168

(3)

Random Walk and Fluctuation Theory

171

(44)

N. H. Bingham

Part I: Random walk on Euclidean space

171

(1)

Introduction

171

(1)

Simple random walk on Z

171

(2)

Recurrence and transience

173

(1)

Simple random walk on Zd; Polya's theorem

174

(1)

Random walks on Rd

175

(2)

Harmonic analysis

177

(1)

Potential theory

177

(2)

Coupling

179

(1)

Renewal theory

179

(1)

Limit theorems and Brownian motion

180

(1)

Conditioned random walks

181

(1)

Part II: Random walks in more general contexts

182

(1)

Random walks and electrical networks

182

(1)

Random walk on graphs

183

(2)

Random walks on groups

185

(3)

Brownian motion on Riemannian manifolds

188

(1)

Random walks on homogeneous spaces, Gelfand pairs, hypergroups and semigroups

189

(1)

Random walk on graphs with special structure

190

(1)

Variants on random walk

191

(2)

Part III: Fluctuation theory

193

(1)

Spitzer's identity

193

(2)

Ladder epochs and heights

195

(2)

Spitzer's arc-sine law

197

(2)

Ballot theorems

199

(1)

Queues

199

(2)

Continuous time

201

(2)

Barrier problems

203

(1)

Higher dimensions and algebraic extensions

204

(1)

Distribution-free results and non-parametric statistics

205

(1)

Postscript

206

(9)

References

206

(9)

A Semigroup Representation and Asymptotic Behavior of Certain Statistics of the Fisher-Wright-Moran Coalescent

215

(34)

Adam Bobrowski

Marek Kimmel

Ovide Arino

Ranajit Chakraborty

Introduction

215

(2)

Markov-chain mutations and genetic drift in populations of varying size

217

(2)

Mathematical preliminaries

219

(3)

The Lyapunov equation and its asymptotic behavior

222

(13)

Stepwise Mutation Model with variable population size

235

(5)

Discussion

240

(2)

Acknowledgements

242

(1)

Appendix

242

(7)

References

246

(3)

Continuous-Time ARMA Processes

249

(28)

P. J. Brockwell

Introduction

249

(2)

CARMA (p, q) processes

251

(5)

ARMA (p, q) processes

256

(3)

Embedding and aliasing

259

(4)

Inference for linear CARMA processes

263

(1)

Nonlinear CAR models

264

(3)

CTAR (p) processes

267

(3)

Inference for CTAR processes

270

(7)

Acknowledgement

275

(1)

References

275

(2)

Record Sequences and their Applications

277

(32)

John Bunge

Charles M. Goldie

Introduction

277

(1)

Partial records

278

(2)

Record values

280

(4)

Sojourns

284

(5)

Record times

289

(3)

Limit theory and strong approximation

292

(3)

Extensions, connections and applications

295

(3)

Random record processes

298

(1)

Poisson paced records

299

(2)

Birth-process paced records

301

(2)

Renewal paced records

303

(3)

Extensions and applications

306

(3)

References

306

(3)

Stochastic Networks with Product Form Equilibrium

309

(56)

Hans Daduna

Introduction

309

(2)

Birth-death processes and exponential networks of queues

311

(6)

Vector-valued birth-death processes and generalized migration processes

317

(5)

Migration processes with concurrent movements and an application of local balance principles

322

(5)

Stochastic ordering and stochastic comparison for network processes

327

(3)

Correlation theory for network processes

330

(4)

Customers of different types, the arrival theorem

334

(5)

Individual customers' sojourn time distributions and passage time distributions

339

(7)

General and symmetric servers: Insensitivity theory

346

(8)

Mixed networks of general exponential and symmetric servers

354

(3)

Complements

357

(8)

References

359

(6)

Stochastic Processes in Insurance and Finance

365

(48)

Paul Embrechts

Rudiger Frey

Hansjorg Furrer

Introduction

365

(8)

Stochastic processes in insurance

373

(16)

Stochastic processes in finance

389

(15)

On the interplay between finance and insurance

404

(9)

Acknowledgements

408

(1)

References

408

(5)

Renewal Theory

413

(30)

D. R. Grey

Introduction

413

(1)

Feller's recurrent events

414

(4)

Theorems of Blackwell, Feller and Orey

418

(2)

Renewal equations

420

(4)

Markov renewal and semi-regenerative processes

424

(1)

Kingman's regenerative phenomena

425

(2)

Superposition of renewal processes

427

(2)

Applications to random walks and branching processes

429

(3)

An inventory model

432

(2)

Stationary increments

434

(2)

Goldie's implicit renewal theory

436

(3)

Schmidli's extension

439

(4)

References

440

(3)

The Kolmogorov Isomorphism Theorem and Extensions to some Nonstationary Processes

443

(28)

Yuichiro Kakihara

Introduction

443

(1)

Stationary processes and the Kolmogorov Isomorphism Theorem

444

(3)

Some classes of nonstationary processes

447

(6)

Weakly harmonizable processes and the Kolmogolov Isomorphism Theorem

453

(2)

Application to estimation and filtering

455

(5)

Multidimensional extension

460

(11)

Acknowledgement

468

(1)

References

468

(3)

Stochastic Processes in Reliability

471

(40)

Masaaki Kijima

Haijun Li

Moshe Shaked

Introduction

471

(1)

Aging first-passage times

472

(11)

Comparison of replacement policies via point processes

483

(12)

Comparison of repairable systems via point processes

495

(3)

A stochastic process approach to failure models in random environments

498

(13)

References

507

(4)

On the supports of Stochastic Processes of Multiplicity One

511

(22)

A. Klopotowski

M. G. Nadkarni

Introduction

511

(1)

Additive decompositions, good sets

512

(3)

Graphs, couples and their unions

515

(2)

Links, linked and uniquely linked sets, loops

517

(5)

Orthogonal decompositions

522

(3)

Connection with dynamics, twisted joinings

525

(1)

Application to the problem of simple Lebesgue spectrum

526

(1)

Walsh functions

527

(6)

Acknowledgements

530

(1)

References

531

(2)

Gaussian Processes: Inequalities, Small Ball Probabilities and Applications

533

(66)

W. V. Li

Q.-M. Shao

Introduction

533

(3)

Inequalities for Gaussian random elements

536

(7)

Small ball probabilities in general setting

543

(13)

Gaussian processes with index set T ⊃ R

556

(7)

Gaussian processes with index set T ⊃ Rd, d ≥ 2

563

(3)

The small ball constants

566

(10)

Applications of small ball probabilities

576

(23)

Acknowledgements

591

(1)

References

592

(7)

Point Processes and Some Related Processes

599

(44)

Robin K. Milne

Introduction

599

(2)

Foundations

601

(17)

Operations on point processes and associated limit results

618

(4)

Some other classes of point process

622

(9)

Statistical inference

631

(4)

Simulation

635

(1)

Concluding remarks

636

(7)

Acknowledgements

637

(1)

References

638

(5)

Characterization and Identifiability for Stochastic Processes

643

(50)

B. L. S. Prakasa Rao

Introduction

643

(1)

Characterizations by properties of stochastic integrals of processes with independent increments

644

(19)

Martingales and conditional structure characterizations

663

(12)

Characterizations for Poisson process as a renewal process and as a point process

675

(9)

Miscellaneous characterizations

684

(9)

Acknowledgement

687

(1)

References

687

(6)

Associated Sequences and Related Inference Problems

693

(40)

B. L. S. Prakasa Rao

Isha Dewan

Introduction

693

(11)

Some probabilistic properties for associated sequences

704

(15)

Random generation of associated sequences

719

(1)

Statistical inference for associated sequences

720

(13)

References

728

(5)

Exchangeability, Functional Equations, and Characterizations

733

(32)

C. R. Rao

D. N. Shanbhag

Introduction

733

(2)

de Finetti's theorem and some related auxiliary results

735

(7)

Functional equations with applications in probability and statistics

742

(13)

Characterizations of mixtures of probability distributions

755

(10)

Acknowledgement

761

(1)

References

761

(4)

Martingales and Some Applications

765

(52)

M. M. Rao

Introduction

765

(2)

Martingale concepts and inequalities

767

(6)

Convergence theorems

773

(5)

Elements of (semi)martingale calculus

778

(15)

An application to likelihood ratios

793

(4)

Exponential (semi)martingales

797

(6)

Applications to financial market models

803

(9)

Remarks on multiparameter and other extensions

812

(5)

References

815

(2)

Markov Chains: Structure and Applications

817

(36)

R. L. Tweedie

Introduction

817

(3)

Countable space chains

820

(11)

General state space chains

831

(12)

Topological spaces

843

(5)

Conclusions

848

(5)

Acknowledgement

849

(1)

References

849

(4)

Diffusion Processes

853

(20)

S. R. S. Varadhan

Brownian motion

853

(2)

Brownian motion as a Markov process

855

(1)

Semigroups and generators

856

(2)

Stochastic integrals

858

(1)

Ito calculus

859

(2)

Brownian motion with a drift

861

(2)

One-dimensional diffusions

863

(5)

The multidimensional case

868

(3)

Diffusions with reflection

871

(2)

References

872

(1)

Ito's Stochastic Calculus and Its Applications

873

(62)

S. Watanabe

Introduction

873

(1)

Semimartingales and stochastic integrals

874

(12)

Stochastic calculus for semimartingales

886

(15)

Stochastic differential equations

901

(19)

Stochastic differential equations on manifolds

920

(15)

References

931

(4)

Subject Index

935

(12)

Contents of Previous Volumes

947


	Buy Textbooks Sell Textbooks College Apparel Shop by School Virtual Bookstores	Order Status Shipping Rates Return Policy Marketplace Info F.A.S.T.	Contact Us Privacy Policy Legal Notices Site Security Employment	Help Desk eCampus Blog Affiliate Program Bulk Orders College Marketing

Need Help? eService@ecampus.com Copyright© 1999-2008
.