Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate them to certain associated Gaussian processes. It builds to this material through self-contained but harmonized 'mini-courses' on the relevant ingredients, which assume only knowledge of measure-theoretic probability. The streamlined selection of topics creates an easy entrance for students and for experts in related fields. The book starts by developing the fundamentals of Markov process theory and then of Gaussian process theory, including...
Written by two foremost researchers in the field, this book studies the local times of Markov processes by employing isomorphism theorems that relate ...
In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally compact Abelian groups and on compact non-Abelian groups. They also obtain many related results. For example, whenever a random Fourier series converges uniformly a.s. it also satisfies the central limit theorem. The methods developed are used to study some questions in harmonic analysis that are not intrinsically random. For example, a new characterization of Sidon sets is derived.
The major results depend heavily on the Dudley-Fernique...
In this book the authors give the first necessary and sufficient conditions for the uniform convergence a.s. of random Fourier series on locally co...
J. Hoffmann Joergen Hoffmann-Joergensen Michael B. Marcus
The title High Dimensional Probability is an attempt to describe the many trib- utaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970's. In each of these fields it is necessary to consider large classes of stochastic processes under minimal conditions. There are rewards in re- search of this sort. One can often gain deep insights, even about familiar processes, by stripping away details that in hindsight turn out to be extraneous. Many of the problems that motivated researchers in the 1970's were solved. But the powerful new tools created...
The title High Dimensional Probability is an attempt to describe the many trib- utaries of research on Gaussian processes and probability in Banach sp...
Jorgen Hoffmann-Jorgensen James Kuelbs Michael B. Marcus
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques- tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop- erties that...
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conferen...
Jorgen Hoffmann-Jorgensen James Kuelbs Michael B. Marcus
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conference on Probability in Banach Spaces, held at Sandjberg, Denmark, August 16-21, 1993. A glance at the table of contents indicates the broad range of topics covered at this conference. What defines research in this field is not so much the topics considered but the generality of the ques- tions that are asked. The goal is to examine the behavior of large classes of stochastic processes and to describe it in terms of a few simple prop- erties that...
The papers contained in this volume are an indication of the topics th discussed and the interests of the participants of The 9 International Conferen...
Joergen Hoffmann-Joergensen Michael B. Marcus Jon A. Wellner
The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces that started in the early 1970s. Many of the problems that motivated researchers at that time were solved. But the powerful new tools created for their solution turned out to be applicable to other important areas of probability. They led to significant advances in the study of empirical processes and other topics in theoretical statistics and to a new approach to the study of aspects of Levy processes and Markov processes in general. The papers...
The title High Dimensional Probability is used to describe the many tributaries of research on Gaussian processes and probability in Banach spaces ...
