EAN: 9781461271116

HIGH DIMENSIONAL PROBABILITY II KARTONIERT (TB)

High dimensional probability  in the sense that encompasses the topics rep resented in this
volume  began about thirty years ago with research in two related areas: limit theorems for
sums of independent Banach space valued random vectors and general Gaussian processes. An
important feature in these past research studies has been the fact that they highlighted the es
sential probabilistic nature of the problems considered. In part  this was because  by working
on a general Banach space  one had to discard the extra  and often extraneous  structure
imposed by random variables taking values in a Euclidean space  or by processes being indexed
by sets in R or Rd. Doing this led to striking advances  particularly in Gaussian process
theory. It also led to the creation or introduction of powerful new tools  such as
randomization  decoupling  moment and exponential inequalities  chaining  isoperimetry and
concentration of measure  which apply to areas well beyond those for which they were created.
The general theory of em pirical processes  with its vast applications in statistics  the study
of local times of Markov processes  certain problems in harmonic analysis  and the general
theory of stochastic processes are just several of the broad areas in which Gaussian process
techniques and techniques from probability in Banach spaces have made a substantial impact.
Parallel to this work on probability in Banach spaces  classical proba bility and empirical
process theory were enriched by the development of powerful results in strong approximations.

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