Ebook: Stochastic Processes and Related Topics: In Memory of Stamatis Cambanis 1943–1995

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.

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Content:
Front Matter....Pages i-xxv
Spectral Representation and Structure of Stable Self-Similar Processes....Pages 1-14
Three Elementary Proofs of the Central Limit Theorem with Applications to Random Sums....Pages 15-23
Almost Everywhere Convergence and SLLN Under Rearrangements....Pages 25-34
Sufficient Conditions for the Existence of Conditional Moments of Stable Random Variables....Pages 35-67
How Heavy are the Tails of a Stationary HARCH(k) Process? A Study of the Moments....Pages 69-102
Use of Stochastic Comparisons in Communication Networks....Pages 103-121
On the Conditional Variance-Covariance of Stable Random Vectors, II....Pages 123-140
Interacting Particle Approximation for Fractal Burgers Equation....Pages 141-166
Optimal Transformations for Prediction in Continuous-Time Stochastic Processes....Pages 167-183
Algebraic Methods Toward Higher-Order Probability Inequalities....Pages 185-206
Comparison and Deviation from a Representation Formula....Pages 207-218
Components of the Strong Markov Property....Pages 219-230
The Russian Options....Pages 231-252
Cycle Representations of Markov Processes: An Application to Rotational Partitions....Pages 253-273
On Extreme Values in Stationary Random Fields....Pages 275-285
Norming Operators for Operator-Self-Similar Processes....Pages 287-295
Multivariate Probability Density and Regression Functions Estimation of Continuous-Time Stationary Processes from Discrete-Time Data....Pages 297-314
Tracing the Path of a Wright-Fisher Process with One-way Mutation in the Case of a Large Deviation....Pages 315-330
A Distribution Inequality For Martingales with Bounded Symmetric Differences....Pages 331-337
Moment Comparison of Multilinear Forms in Stable and Semistable Random Variables with Application to Semistable Multiple Integrals....Pages 339-355
Global Dependency Measure for Sets of Random Elements: “The Italian Problem” and Some Consequences....Pages 357-375

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Content:
Front Matter....Pages i-xxv
Spectral Representation and Structure of Stable Self-Similar Processes....Pages 1-14
Three Elementary Proofs of the Central Limit Theorem with Applications to Random Sums....Pages 15-23
Almost Everywhere Convergence and SLLN Under Rearrangements....Pages 25-34
Sufficient Conditions for the Existence of Conditional Moments of Stable Random Variables....Pages 35-67
How Heavy are the Tails of a Stationary HARCH(k) Process? A Study of the Moments....Pages 69-102
Use of Stochastic Comparisons in Communication Networks....Pages 103-121
On the Conditional Variance-Covariance of Stable Random Vectors, II....Pages 123-140
Interacting Particle Approximation for Fractal Burgers Equation....Pages 141-166
Optimal Transformations for Prediction in Continuous-Time Stochastic Processes....Pages 167-183
Algebraic Methods Toward Higher-Order Probability Inequalities....Pages 185-206
Comparison and Deviation from a Representation Formula....Pages 207-218
Components of the Strong Markov Property....Pages 219-230
The Russian Options....Pages 231-252
Cycle Representations of Markov Processes: An Application to Rotational Partitions....Pages 253-273
On Extreme Values in Stationary Random Fields....Pages 275-285
Norming Operators for Operator-Self-Similar Processes....Pages 287-295
Multivariate Probability Density and Regression Functions Estimation of Continuous-Time Stationary Processes from Discrete-Time Data....Pages 297-314
Tracing the Path of a Wright-Fisher Process with One-way Mutation in the Case of a Large Deviation....Pages 315-330
A Distribution Inequality For Martingales with Bounded Symmetric Differences....Pages 331-337
Moment Comparison of Multilinear Forms in Stable and Semistable Random Variables with Application to Semistable Multiple Integrals....Pages 339-355
Global Dependency Measure for Sets of Random Elements: “The Italian Problem” and Some Consequences....Pages 357-375
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