Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edit...
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ISBN:
(数字)9783110218091
ISBN:
(纸本)9783110218084
Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms. For the present second edition, the authors not only revised the existing text, but also added some new sections as well as several exercises with solutions. The book addresses to researchers and graduate students who wish to comprehend the area of Dirichlet forms and symmetric Markov processes.
Lambert W-function is relatively a new special function with applications in various areas of mathematics, statistics and engineering. In this paper, some new applications of W-function are given in probability and st...
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Lambert W-function is relatively a new special function with applications in various areas of mathematics, statistics and engineering. In this paper, some new applications of W-function are given in probability and statistics (generalized gamma distribution and special cases, inverse generalized gamma distribution and special cases, generalized extreme value distribution, order statistics, etc.), mathematics, information theory and hydraulics. Computation of W-function, with good precision, is already available in Mathematica and Maple softwares for numerical applications.
In this book, limit theorems are made accessibly by stating everything in terms of a game of tossing a coin: heads or tails. This book is suitable for anyone who would like to learn more about mathematical probabili...
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ISBN:
(数字)9781470421397
ISBN:
(纸本)9780821837146
In this book, limit theorems are made accessibly by stating everything in terms of a game of tossing a coin: heads or tails. This book is suitable for anyone who would like to learn more about mathematical probability and has a one-year undergraduate course in analysis.
The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry. The developm...
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ISBN:
(数字)9781470413842
ISBN:
(纸本)9780821848203
The material covered in this book involves important and non-trivial results in contemporary probability theory motivated by polymer models, as well as other topics of importance in physics and chemistry. The development carefully provides the basic definitions of mutual intersection and self-intersection local times for Brownian motions and the accompanying large deviation results. The book then proceeds to the analogues of these concepts and results for random walks on lattices of $R^d$. This includes suitable integrability and large deviation results for these models and some applications. Moreover, the notes and comments at the end of the chapters provide interesting remarks and references to various related results, as well as a good number of exercises. The author provides a beautiful development of these subtle topics at a level accessible to advanced graduate students.
This book is based on lectures presented by the author at DePaul University in July 1986. The lectures cover three main topics. The first is local time theory for Brownian motion and some geometrical inequalities for ...
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ISBN:
(数字)9781470424305
ISBN:
(纸本)9780821807217
This book is based on lectures presented by the author at DePaul University in July 1986. The lectures cover three main topics. The first is local time theory for Brownian motion and some geometrical inequalities for harmonic functions in the upper half-plane $R^{n+1}_+$. The author sketches a proof of the inequalities obtained by Barlow and Yor for the maximal local time functional. The second topic concerns a probabilistic treatment of Riesz transforms in $R^{n+1}_+$, and semimartingale inequalities. The author proves semimartingale inequalities of the type usually obtained for martingales. The final topic centers on a discussion of the Ornstein-Uhlenbeck semigroup and P. A. Meyer's extension of the Riesz inequalities for the infinite-dimensional version of this semigroup. One of the major results of the book is the establishment of inequalities for the density of the area integral.
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