Markov Processes and Related Topics: A Festschrift for Thomas G. Kurtz
Editor: Stewart N. Ethier
Editor: Jin Feng
Editor: Richard H. Stockbridge
Collections, Volume 4
Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008.
A four-day conference, “Markov Processes and Related Topics,” was held at the University of Wisconsin–Madison July 10–13, 2006, in celebration of Tom Kurtz’s 65th birthday and his many contributions to mathematics. Speakers were invited to submit a paper to this collection, and after a lengthy refereeing and editing process, the present “Festschrift” volume has emerged. Its diversity of topics is a reflection of the wide range of subjects to which Tom has contributed.
Tom Kurtz was born in Kansas City on July 14, 1941. He graduated from La Plata High School in La Plata, Missouri, in 1959, earned a B.A. degree from the University of Missouri in 1963, and completed his Ph.D. in mathematics at Stanford University in 1967 under the supervision of James McGregor. That same year he began his career at the University of Wisconsin–Madison, where he remained through his retirement in 2008. He became Professor of Mathematics in 1975, Professor of Statistics in 1985, and Paul Lévy Professor of Mathematics and Statistics in 1996. Over the course of his career, he served his profession in numerous capacities, including Director of the Center for the Mathematical Sciences (1990–1996), Editor of the Annals of Probability (2000–2002), and President of the Institute of Mathematical Statistics (2005–2006). He organized the Summer Intern Program in Probability for nearly a decade; this program had a significant impact on the next generation of probabilists.
Tom has published some 90 papers (with 46 distinct coauthors), two books, and two sets of lecture notes, and he has had 26 Ph.D. students. A complete list is provided beginning on page ix. Topics to which Tom has contributed include
• operator semigroup theory: 2, 4, 9, 12, 15, 19, 21, 22, 25, 36.
• theory of Markov processes: 13, 33, 44, 67.
• limit theorems for Markov processes: 3, 6, 7, 8, 10, 18, 20, 23, 29, 31, 32, 34, 35, 37, 45, 46, 50, 51, 60, 85.
• stochastic equations: 28, 49, 59, 73, 82, 83, 87, 91.
• filtering: 38, 39, 43, 77.
• stochastic control: 42, 47, 68, 75, 79.
• queueing theory: 58, 61, 64, 66, 70, 86.
• branching processes: 5, 14, 24, 65, 90.
• point processes: 17, 88.
• population genetics models: 30, 41, 48, 53, 55, 57, 62, 63, 69, 74, 76, 80, 81.
• other population processes: 56, 71, 72, 84, 89.
• miscellaneous probability theory: 11, 16, 26, 27.
• analysis of algorithms: 40, 52, 54, 78.
• fluid mechanics: 1.
The conference was sponsored by the National Science Foundation, the National Security Agency, the U.S. Army Research Office, the Office of Naval Research, the UW–Madison Departments of Mathematics and Statistics, the UW–Milwaukee Department of Mathematical Sciences, and the Institute of Mathematical Statistics. We are grateful for their help in making the conference, and therefore this volume, possible.
Digital Object Identifiers: doi:10.1214/074921708
Copyright © 2008, Institute of Mathematical Statistics.
The Decomposition-Separation Theorem for Finite Nonhomogeneous Markov Chains and Related Problems
Isaac M. Sonin; 1-15
Conditional Limit Laws and Inference for Generation Sizes of Branching Processes
P. E. Ney, and A. N. Vidyashankar; 17-30
Absorption Time Distribution for an Asymmetric Random Walk
S. N. Ethier; 31-40
Fractional Stability of Diffusion Approximation for Random Differential Equations
Yuriy V. Kolomiets; 41-61
From Particles with Random Potential to a Nonlinear Vlasov–Fokker–Planck Equation
Jin Feng; 63-83
Diffusion Processes on Manifolds
Fabrice Debbasch, and Claire Chevalier; 85-97
Stochastic Equations Driven by a Cauchy Process
Vladimir P. Kurenok; 99-106
On Detecting Fake Coin Flip Sequences
Michael A. Kouritzin, Fraser Newton, Sterling Orsten, and Daniel C. Wilson; 107-122
A Class of Multivariate Micromovement Models of Asset Price and Their Bayesian Model Selection via Filtering
Laurie C. Scott, and Yong Zeng; 123-136
Determining the Optimal Control of Singular Stochastic Processes Using Linear Programming
Kurt Helmes, and Richard H. Stockbridge; 137-153
A Degenerate Variance Control Problem with Discretionary Stopping
Daniel Ocone, and Ananda Weerasinghe; 155-167
Double Skorokhod Map and Reneging Real-Time Queues
Łukasz Kruk, John Lehoczky, Kavita Ramanan, and Steven Shreve; 169-193
Bounding Stationary Expectations of Markov Processes
Peter W. Glynn, and Assaf Zeevi; 195-214
Internet Traffic and Multiresolution Analysis
Ying Zhang, Zihui Ge, Suhas Diggavi, Z. Morley Mao, Matthew Roughan, Vinay Vaishampayan, Walter Willinger, and Yin Zhang; 215-234
Maximum Queue Length of a Fluid Model with an Aggregated Fractional Brownian Input
Tyrone E. Duncan, and Yasong Jin; 235-251
Fluid Model for a Data Network with α-Fair Bandwidth Sharing and General Document Size Distributions: Two Examples of Stability
H. C. Gromoll, and R. J. Williams; 253-265
No Arbitrage and General Semimartingales
Philip Protter, and Kazuhiro Shimbo; 267-283
Optimal Asset Allocation under Forward Exponential Performance Criteria
Marek Musiela, and Thaleia Zariphopoulou; 285-300
Estimates of Dynamic VaR and Mean Loss Associated to Diffusion Processes
Laurent Denis, Begoña Fernández, and Ana Meda; 301-314