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2007 | Book

Memoirs of My Research on Stochastic Analysis Read chapter Read first chapter

Stochastic Analysis and Applications

The Abel Symposium 2005

Editors: Fred Espen Benth, Giulia Di Nunno, Tom Lindstrøm, Bernt Øksendal, Tusheng Zhang

Publisher: Springer Berlin Heidelberg

Book Series : Abel Symposia

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

Kiyosi Ito, the founder of stochastic calculus, is one of the few central figures of the twentieth century mathematics who reshaped the mathematical world. Today stochastic calculus is a central research field with applications in several other mathematical disciplines, for example physics, engineering, biology, economics and finance.

The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over the world were invited to present the newest developments within the exciting and fast growing field of stochastic analysis. The present volume combines both papers from the invited speakers and contributions by the presenting lecturers.

A special feature is the Memoirs that Kiyoshi Ito wrote for this occasion. These are valuable pages for both young and established researchers in the field.

Table of Contents

Frontmatter
Memoirs of My Research on Stochastic Analysis
Kiyosi Itô
Itô Calculus and Quantum White Noise Calculus
Luigi Accardi, Andreas Boukas
Homogenization of Diffusions on the Lattice Zd with Periodic Drift Coefficients, Applying a Logarithmic Sobolev Inequality or a Weak Poincaré Inequality
Sergio Albeverio, M. Simonetta Bernabei, Michael Röckner, Minoru W. Yoshida
Theory and Applications of Infinite Dimensional Oscillatory Integrals
Sergio Albeverio, Sergio Albeverio
Ambit Processes; with Applications to Turbulence and Tumour Growth
Ole E. Barndorff-Nielsen, Jürgen Schmiegel
A Stochastic Control Approach to a Robust Utility Maximization Problem
Giuliana Bordigoni, Anis Matoussi, Martin Schweizer
Extending Markov Processes in Weak Duality by Poisson Point Processes of Excursions
Zhen-Qing Chen, Masatoshi Fukushima, Jiangang Ying
Hedging with Options in Models with Jumps
Rama Cont, Peter Tankov, Ekaterina Voltchkova
Power Variation Analysis of Some Integral Long-Memory Processes
José Manuel Corcuera
Kolmogorov Equations for Stochastic PDE's with Multiplicative Noise
Giuseppe Da Prato
Stochastic Integrals and Adjoint Derivatives
Giulia Di Nunno, Yuri A. Rozanov
An Application of Probability to Nonlinear Analysis
Eugene B. Dynkin
The Space of Stochastic Differential Equations
K. David Elworthy
Extremes of supOU Processes
Vicky Fasen, Claudia Klüppelberg
Gaussian Bridges
Dario Gasbarra, Tommi Sottinen, Esko Valkeila
Some of the Recent Topics on Stochastic Analysis
Takeyuki Hida
Differential Equations Driven by Hölder Continuous Functions of Order Greater than 1/2
Yaozhong Hu, David Nualart
On Asymptotics of Banach Space-valued Itô Functionals of Brownian Rough Paths
Yuzurui Inahama, Hiroshi Kawab
Continuous-Time Markowitz's Problems in an Incomplete Market, with No-Shorting Portfolios
Hanqing Jin, Xun Yu Zhou
Quantum and Classical Conserved Quantities: Martingales, Conservation Laws and Constants of Motion
Torbjørn Kolsrud
Different Lattice Approximations for Hôegh-Krohn's Quantum Field Model
Song Liang
Itô Atlas, its Application to Mathematical Finance and to Exponentiation of Infinite Dimensional Lie Algebras
Paul Malliavin
The Invariant Distribution of a Diffusion: Some New Aspects
Henry P. McKean
Formation of Singularities in Madelung Fluid: A Nonconventional Application of Itô Calculus to Foundations of Quantum Mechanics
Laura M. Morato
G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type
Shige Peng
Perpetual Integral Functionals of Diffusions and their Numerical Computations
Paavo Salminen, Olli Wallin
Chaos Expansions and Malliavin Calculus for Lévy Processes
Josep Lluís Solé, Frederic Utzet, Josep Vives
Study of Simple but Challenging Diffusion Equation
Daniel W. Stroock
Itô Calculus and Malliavin Calculus
Shinzo Watanabe
The Malliavin Calculus for Processes with Conditionally Independent Increments
Aleh L. Yablonski
Metadata
Title
Stochastic Analysis and Applications
Editors
Fred Espen Benth
Giulia Di Nunno
Tom Lindstrøm
Bernt Øksendal
Tusheng Zhang
Copyright Year
2007
Publisher
Springer Berlin Heidelberg
Electronic ISBN
978-3-540-70847-6
Print ISBN
978-3-540-70846-9
DOI
https://doi.org/10.1007/978-3-540-70847-6