Stochastic Processes and Related Topics

1. Front Matter

   Pages i-xxv

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2. Spectral Representation and Structure of Stable Self-Similar Processes

   • K. Burnecki, J. Rosiński, A. Weron

   Pages 1-14

3. Three Elementary Proofs of the Central Limit Theorem with Applications to Random Sums

   • T. Cacoullos, N. Papadatos, V. Papathanasiou

   Pages 15-23

4. Almost Everywhere Convergence and SLLN Under Rearrangements

   • Sergei Chobanyan, V. Mandrekar

   Pages 25-34

5. Sufficient Conditions for the Existence of Conditional Moments of Stable Random Variables

   • Renata Cioczek-Georges, Murad S. Taqqu

   Pages 35-67

6. How Heavy are the Tails of a Stationary HARCH(k) Process? A Study of the Moments

   • Paul Embrechts, Gennady Samorodnitsky, Michel M. Dacorogna, Ulrich A. Müller

   Pages 69-102

7. Use of Stochastic Comparisons in Communication Networks

   • A. Ephremides

   Pages 103-121

8. On the Conditional Variance-Covariance of Stable Random Vectors, II

   • Stergios B. Fotopoulos

   Pages 123-140

9. Interacting Particle Approximation for Fractal Burgers Equation

   • T. Funaki, W. A. Woyczyński

   Pages 141-166

10. Optimal Transformations for Prediction in Continuous-Time Stochastic Processes

    • B. Gidas, A. Murua

    Pages 167-183

11. Algebraic Methods Toward Higher-Order Probability Inequalities

    • Kenneth I. Gross, Donald St. P. Richards

    Pages 185-206

12. Comparison and Deviation from a Representation Formula

    • Christian Houdré

    Pages 207-218

13. Components of the Strong Markov Property

    • Olav Kallenberg

    Pages 219-230

14. The Russian Options

    • G. Kallianpur

    Pages 231-252

15. Cycle Representations of Markov Processes: An Application to Rotational Partitions

    • S. Kalpazidou

    Pages 253-273

16. On Extreme Values in Stationary Random Fields

    • M. R. Leadbetter, Holger Rootzén

    Pages 275-285

17. Norming Operators for Operator-Self-Similar Processes

    • Makoto Maejima

    Pages 287-295

18. Multivariate Probability Density and Regression Functions Estimation of Continuous-Time Stationary Processes from Discrete-Time Data

    • Elias Masry

    Pages 297-314

19. Tracing the Path of a Wright-Fisher Process with One-way Mutation in the Case of a Large Deviation

    • F. Papangelou

    Pages 315-330

20. A Distribution Inequality For Martingales with Bounded Symmetric Differences

    • Loren D. Pitt

    Pages 331-337

In the last twenty years extensive research has been devoted to a better understanding of the stable and other closely related infinitely divisible mod­ els. Stamatis Cambanis, a distinguished educator and researcher, played a special leadership role in the development of these research efforts, particu­ larly related to stable processes from the early seventies until his untimely death in April '95. This commemorative volume consists of a collection of research articles devoted to reviewing the state of the art of this and other rapidly developing research and to explore new directions of research in these fields. The volume is a tribute to the Life and Work of Stamatis by his students, friends, and colleagues whose personal and professional lives he has deeply touched through his generous insights and dedication to his profession. Before the idea of this volume was conceived, two conferences were held in the memory of Stamatis. The first was organized by the University of Athens and the Athens University of Economics and was held in Athens during December 18-19, 1995. The second was a significant part of a Spe­ cial IMS meeting held at the campus of the University of North Carolina at Chapel Hill during October 17-19, 1996. It is the selfless effort of sev­ eral people that brought about these conferences. We believe that this is an appropriate place to acknowledge their effort; and on behalf of all the participants, we extend sincere thanks to all these persons.

• Finite
• Markov process
• Markov property
• Martingal
• Martingale
• Moment
• Random variable
• Rang
• Variance
• continuous-time stochastic process
• mathematics
• probability
• self-similar process
• stochastic process
• stochastic processes

• Departments of Mathematics & Statistics, Columbia University, New York, UK

  Ioannis Karatzas

• Department of Mathematics, University of Tennessee, Knoxville, USA

  Balram S. Rajput

• Department of Mathematics, Boston University, Boston, USA

  Murad S. Taqqu

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