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From Classical to Modern Probability

CIMPA Summer School 2001. 'Progress in Probability'. Auflage 2003. Book. Sprache: Englisch.
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This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as ma... weiterlesen
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From Classical to Modern Probability als Buch
Produktdetails
Titel: From Classical to Modern Probability

ISBN: 3764321695
EAN: 9783764321697
CIMPA Summer School 2001.
'Progress in Probability'.
Auflage 2003.
Book.
Sprache: Englisch.
Herausgegeben von Pierre Picco, Jaime San Martin
Birkhäuser Basel

24. Oktober 2003 - gebunden - 240 Seiten

Beschreibung

This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields.

Inhaltsverzeichnis

Asymptotic of the Heat Kernel in Unbounded Domains.- 1 Introduction.- 2 Ratio theorem for domains with harmonic cone C? of dimension 1.- 3 Benedicks domains.- References.- Spin Systems with Long Range Interactions.- 1 Ising spin systems.- 2 Phase transition.- 3 Time evolution.- References.- Nonlinear Dirichlet Problem and Nonlinear Integration.- 1 Generalities.- 2 Preliminaries on capacities.- 3 Radon capacities.- 4 Lusin capacities.- 5 Answering the questions and last words.- References.- First-Passage Percolation.- 1 The basic model and the shape model.- 2 Exponential bounds for large deviations.- 3 Bounds of moderate deviations.- References.- Central Limit Theorem for Markov Processes.- 1 Introduction.- 2 A warming-up example.- 3 Central limit theorem for Markov processs.- 4 Regularity of the diffusion coefficient.- References.- Stochastic Orders and Stopping Times in Brownian Motion.- 1 Introduction.- 2 Martingales and stochastic orders.- 3 Skorohod embeddings in standard Brownian motion.- 4 A maximal property of Azéma-Yor stopped Brownian motion.- 5 Practical description of the optimal stopping time for the look-back American put option problem.- References.
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