Stochastic Analysis and Applications: The Abel Symposium 2005

✍ Scribed by Kiyosi Itô (auth.), Fred Espen Benth, Giulia Di Nunno, Tom Lindstrøm, Bernt Øksendal, Tusheng Zhang (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2007
• Tongue: English
• Leaves: 672
• Series: Abel Symposia 2
• Edition: 1
• Category: Library

✦ Synopsis

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

Front Matter....Pages I-XI
Memoirs of My Research on Stochastic Analysis....Pages 1-6
Itô Calculus and Quantum White Noise Calculus....Pages 7-51
Homogenization of Diffusions on the Lattice Zd with Periodic Drift Coefficients, Applying a Logarithmic Sobolev Inequality or a Weak Poincaré Inequality....Pages 53-72
Theory and Applications of Infinite Dimensional Oscillatory Integrals....Pages 73-91
Ambit Processes; with Applications to Turbulence and Tumour Growth....Pages 93-124
A Stochastic Control Approach to a Robust Utility Maximization Problem....Pages 125-151
Extending Markov Processes in Weak Duality by Poisson Point Processes of Excursions....Pages 153-196
Hedging with Options in Models with Jumps....Pages 197-217
Power Variation Analysis of Some Integral Long-Memory Processes....Pages 219-234
Kolmogorov Equations for Stochastic PDE's with Multiplicative Noise....Pages 235-263
Stochastic Integrals and Adjoint Derivatives....Pages 265-307
An Application of Probability to Nonlinear Analysis....Pages 309-325
The Space of Stochastic Differential Equations....Pages 327-337
Extremes of supOU Processes....Pages 339-359
Gaussian Bridges....Pages 361-382
Some of the Recent Topics on Stochastic Analysis....Pages 383-397
Differential Equations Driven by Hölder Continuous Functions of Order Greater than 1/2....Pages 399-413
On Asymptotics of Banach Space-valued Itô Functionals of Brownian Rough Paths....Pages 415-434
Continuous-Time Markowitz's Problems in an Incomplete Market, with No-Shorting Portfolios....Pages 435-459
Quantum and Classical Conserved Quantities: Martingales, Conservation Laws and Constants of Motion....Pages 461-491
Different Lattice Approximations for Hôegh-Krohn's Quantum Field Model....Pages 493-499
Itô Atlas, its Application to Mathematical Finance and to Exponentiation of Infinite Dimensional Lie Algebras....Pages 501-514
The Invariant Distribution of a Diffusion: Some New Aspects....Pages 515-526
Formation of Singularities in Madelung Fluid: A Nonconventional Application of Itô Calculus to Foundations of Quantum Mechanics....Pages 527-540
G -Expectation, G -Brownian Motion and Related Stochastic Calculus of Itô Type....Pages 541-567
Perpetual Integral Functionals of Diffusions and their Numerical Computations....Pages 569-594
Chaos Expansions and Malliavin Calculus for Lévy Processes....Pages 595-612
Study of Simple but Challenging Diffusion Equation....Pages 613-621
Itô Calculus and Malliavin Calculus....Pages 623-639
The Malliavin Calculus for Processes with Conditionally Independent Increments....Pages 641-678

✦ Subjects

Probability Theory and Stochastic Processes;Analysis;Statistical Theory and Methods;Quantitative Finance;Mathematical and Computational Physics;Appl.Mathematics/Computational Methods of Engineering