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.
Part I. Foundations and techniques in stochastic analysis: 1. Random variables - without basic space Gotz Kersting
2. Chaining techniques and their application to stochastic flows Michael Scheutzow
3. Ergodic properties of a class of non-Markovian processes Martin Hairer
4. Why study multifractal spectra? Peter Morters
Part II. Construction, simulation, discretisation of stochastic processes: 5, Construction of surface measures for Brownian motion Nadia Sidorova and Olaf Wittich
6. Sampling conditioned diffusions Martin Hairer, Andrew Stuart and Jochen Vobeta
7. Coding and convex optimization problems Steffen Dereich
Part III. Stochastic analysis in mathematical physics: 8. Intermittency on catalysts Jurgen Gartner, Frank den Hollander and Gregory Maillard
9. Stochastic dynamical systems in infinite dimensions Salah-Eldin A. Mohammed
10. Feynman formulae for evolutionary equations Oleg G.Smolyanov
11. Deformation quantization in infinite dimensional analysis Remi Leandre
Part IV. Stochastic analysis in mathematical biology: 12. Measure-valued diffusions, coalescents and genetic inference Matthias Birkner and Jochen Blath
13. How often does the ratchet click? Facts, heuristics, asymptotics Alison M. Etheridge, Peter Pfaffelhuber and Anton Wakolbinger.