Trends in Stochastic Analysis

doi:10.1017/CBO9781139107020

Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Written by leading experts in the field, the articles cover a wide range of topics, ranging from an alternative set-up of rigorous probability to the sampling of conditioned diffusions. Applications in physics and biology are treated, with discussion of Feynman formulas, intermittency of Anderson models and genetic inference. A large number of the articles are topical surveys of probabilistic tools such as chaining techniques, and of research fields within stochastic analysis, including stochastic dynamics and multifractal analysis. Showcasing the diversity of research activities in the field, this book is essential reading for any student or researcher looking for a guide to modern trends in stochastic analysis and neighbouring fields.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp 1-2
- By Jochen Blath, Peter Mörters, Michael Scheutzowf
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Heinrich von Weizsäcker's students
pp 3-4
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Heinrich von Weizsäcker's publications
pp 5-10
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I - Foundations and techniques in stochastic analysis
pp 11-12
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1 - Random variables – without basic space
pp 13-34
- By Götz Kersting, Universität Frankfurt
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2 - Chaining techniques and their application to stochastic flows
pp 35-64
- By Michael Scheutzow, Universität Berlin
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3 - Ergodic properties of a class of non-Markovian processes
pp 65-98
- By Martin Hairer, University of Warwick
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4 - Why study multifractal spectra?
pp 99-120
- By Peter Mörters, University of Bath
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II - Construction, simulation, discretization of stochastic processes
pp 121-122
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5 - Construction of surface measures for Brownian motion
pp 123-158
- By Nadia Sidorova, University College London, Olaf Wittich, Universiteit Eindhoven
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6 - Sampling conditioned diffusions
pp 159-186
- By Martin Hairer, University of Warwick, Andrew Stuart, University of Warwick, Jochen Voß, University of Warwick
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7 - Asymptotic formulae for coding problems: a review
pp 187-232
- By Steffen Dereich, University of Bath
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III - Stochastic analysis in mathematical physics
pp 233-234
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8 - Intermittency on catalysts
pp 235-248
- By Jürgen Gärtner, Universität Berlin, Frank den Hollander, Leiden University, Grégory Maillard, Ecole Polytechnique Fédérale de Lausanne
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9 - Stochastic dynamical systems in infinite dimensions
pp 249-282
- By Salah-Eldin A. Mohammed, Illinois University
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10 - Feynman formulae for evolutionary equations
pp 283-302
- By Oleg G. Smolyanov, Moscow State University
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11 - Deformation quantization in infinite dimensional analysis
pp 303-326
- By Rémi Léandre, Université de Bourgogne
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IV - Stochastic analysis in mathematical biology
pp 327-328
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12 - Measure-valued diffusions, coalescents and genetic inference
pp 329-364
- By Matthias Birkner, Stochastik Mohrenstraße, Jochen Blath, Universität Berlin
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13 - How often does the ratchet click? Facts, heuristics, asymptotics
pp 365-390
- By Alison M. Etheridge, University of Oxford, Peter Pfaffelhuber, University of Munich, Anton Wakolbinger, J.W. Goethe-Universität
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Trends in Stochastic Analysis

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp 1-2

Heinrich von Weizsäcker's students
pp 3-4

Heinrich von Weizsäcker's publications
pp 5-10

I - Foundations and techniques in stochastic analysis
pp 11-12

1 - Random variables – without basic space
pp 13-34

2 - Chaining techniques and their application to stochastic flows
pp 35-64

3 - Ergodic properties of a class of non-Markovian processes
pp 65-98

4 - Why study multifractal spectra?
pp 99-120

II - Construction, simulation, discretization of stochastic processes
pp 121-122

5 - Construction of surface measures for Brownian motion
pp 123-158

6 - Sampling conditioned diffusions
pp 159-186

7 - Asymptotic formulae for coding problems: a review
pp 187-232

III - Stochastic analysis in mathematical physics
pp 233-234

8 - Intermittency on catalysts
pp 235-248

9 - Stochastic dynamical systems in infinite dimensions
pp 249-282

10 - Feynman formulae for evolutionary equations
pp 283-302

11 - Deformation quantization in infinite dimensional analysis
pp 303-326

IV - Stochastic analysis in mathematical biology
pp 327-328

12 - Measure-valued diffusions, coalescents and genetic inference
pp 329-364

13 - How often does the ratchet click? Facts, heuristics, asymptotics
pp 365-390

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