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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.



Memoirs of My Research on Stochastic Analysis

Without Abstract
Kiyosi Itô

Itô Calculus and Quantum White Noise Calculus

Without Abstract
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

Without Abstract
Sergio Albeverio, M. Simonetta Bernabei, Michael Röckner, Minoru W. Yoshida

Theory and Applications of Infinite Dimensional Oscillatory Integrals

Without Abstract
Sergio Albeverio, Sergio Albeverio

Ambit Processes; with Applications to Turbulence and Tumour Growth

Without Abstract
Ole E. Barndorff-Nielsen, Jürgen Schmiegel

A Stochastic Control Approach to a Robust Utility Maximization Problem

Without Abstract
Giuliana Bordigoni, Anis Matoussi, Martin Schweizer

Extending Markov Processes in Weak Duality by Poisson Point Processes of Excursions

Without Abstract
Zhen-Qing Chen, Masatoshi Fukushima, Jiangang Ying

Hedging with Options in Models with Jumps

Without Abstract
Rama Cont, Peter Tankov, Ekaterina Voltchkova

Power Variation Analysis of Some Integral Long-Memory Processes

Without Abstract
José Manuel Corcuera

Kolmogorov Equations for Stochastic PDE's with Multiplicative Noise

Without Abstract
Giuseppe Da Prato

Stochastic Integrals and Adjoint Derivatives

Without Abstract
Giulia Di Nunno, Yuri A. Rozanov

An Application of Probability to Nonlinear Analysis

Without Abstract
Eugene B. Dynkin

The Space of Stochastic Differential Equations

Without Abstract
K. David Elworthy

Extremes of supOU Processes

Without Abstract
Vicky Fasen, Claudia Klüppelberg

Gaussian Bridges

Without Abstract
Dario Gasbarra, Tommi Sottinen, Esko Valkeila

Some of the Recent Topics on Stochastic Analysis

Without Abstract
Takeyuki Hida

Differential Equations Driven by Hölder Continuous Functions of Order Greater than 1/2

Without Abstract
Yaozhong Hu, David Nualart

On Asymptotics of Banach Space-valued Itô Functionals of Brownian Rough Paths

Without Abstract
Yuzurui Inahama, Hiroshi Kawab

Continuous-Time Markowitz's Problems in an Incomplete Market, with No-Shorting Portfolios

Without Abstract
Hanqing Jin, Xun Yu Zhou

Quantum and Classical Conserved Quantities: Martingales, Conservation Laws and Constants of Motion

Without Abstract
Torbjørn Kolsrud

Different Lattice Approximations for Hôegh-Krohn's Quantum Field Model

Without Abstract
Song Liang

Itô Atlas, its Application to Mathematical Finance and to Exponentiation of Infinite Dimensional Lie Algebras

Without Abstract
Paul Malliavin

The Invariant Distribution of a Diffusion: Some New Aspects

Without Abstract
Henry P. McKean

Formation of Singularities in Madelung Fluid: A Nonconventional Application of Itô Calculus to Foundations of Quantum Mechanics

Without Abstract
Laura M. Morato

G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type

Without Abstract
Shige Peng

Perpetual Integral Functionals of Diffusions and their Numerical Computations

Without Abstract
Paavo Salminen, Olli Wallin

Chaos Expansions and Malliavin Calculus for Lévy Processes

Without Abstract
Josep Lluís Solé, Frederic Utzet, Josep Vives

Study of Simple but Challenging Diffusion Equation

Without Abstract
Daniel W. Stroock

Itô Calculus and Malliavin Calculus

Without Abstract
Shinzo Watanabe

The Malliavin Calculus for Processes with Conditionally Independent Increments

Without Abstract
Aleh L. Yablonski
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